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DESIGN AND ANALYSIS OF HIGHEFFICIENCY L-BAND POWER AMPLIFIERSThesis by Feiyu Wang In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2006 (Defended December 19, 2005) ii © 2006 Feiyu Wang All Rights Reserved iii ACKNOWLEDGEMENTS First of all, I would like to acknowledge the guidance, support and patience from my advisor Prof. David Rutledge. His knowledge and wisdom have guided me in my research; his continuous support and encouragement have helped me through many challenging situations. I appreciate this wonderful opportunity to study and work in the MMIC group at Caltech. I would also like to thank Dr. Sander Weinreb for helpful advice during the past four years. I have learned many different aspects of microwave and millimeter-wave engineering from him. I am equally grateful for Prof. Almudena Suarez’s guidance in the study of the stability analysis. It would not be possible to tackle such a difficult topic without her advice and energy. Special appreciation goes to Dale Yee, “my advisor of everything else.” With her kind advice, I saved much time in everyday life, so I can focus my attention on research. It was a great pleasure to work with the following individuals from the Jet Propulsion Laboratory (JPL), Pasadena, CA: Wendy Edelstein, Dr. Alina Moussessian, and Constantine Andricos. Their support and encouragement are appreciated. Sanggeon Jeon deserves special acknowledgement for numerous helpful conversations and discussions during the past three years. He has been a wonderful friend, colleague, and teacher. I would like to thank Kent Potter and some former students in the group: Dr. Ichiro Aoki, Dr. Lawrence Cheung, Dr. Scott Kee, Dr. Dai Lu, and Dr. Matthew Morgan. I appreciate the time and patience they have spent to teach me many different aspects of microwave and power amplifier designs. I would also like to thank the following individuals for helpful discussions: Joe Bardin, Patrick Cesorano, Dr. Younkyu Chung, Glenn Jones, Prof. Bumman Kim, Dr. Seungwoo iv Kim, Sébestien Lasfargues, Min Park, Ann Shen, Edwin Soedarmadji, Yulung Tang, Takahiro Taniguchi, and Nikalas Wadefalk. I would like to thank Prof. Ali Hajimiri and former and current students in his group for helpful discussions. They are Dr. Xiang Guan, Dr. Roberto Aparicio, Prof. Hui Wu, Dr. Chris White, Dr. Behnam Analui, Prof. Donhee Ham, Prof. Hossein Hashemi, Ehsan Afshari, Arun Natarajan, and Abbas Komijani. I would like to acknowledge the members of the candidacy exam committee: Prof. John Doyle, Dr. Alina Moussessian, Prof. David Rutledge, Prof. Kerry Vahala, and Prof. Changhuei Yang. I am equally grateful to the members of the thesis defense exam committee: Prof. William Bridges, Dr. Alina Moussessian, Prof. David Rutledge, Prof. Kerry Vahala, and Dr. Sander Weinreb. I would like to thank Carol Sosnowski, Linda Dosza, Heather Hein, Patama Taweesup, and Lyn Hein, and other staff members in the Department of Electrical Engineering, for their contribution has made my work much easier. I want to thank the Caltech institution for providing me with an opportunity to pursue my M.S. and Ph.D. degrees. I want to acknowledge the financial support from Caltech, Lee Center, and JPL. To my parents, who have shown great love and continuous support in every step of my life, I appreciate everything they have done for me. To Ms. Margaret Wong, my advisor at Breck School, Minneapolis, MN, I would never have come to this stage of academic career without her generous help. To my undergraduate research advisor, Prof. William Jemison, I would like to thank him for introducing me to the world of microwave engineering. Most of all, I would like to thank my wife, Jia Fan. Beyond a supporter, she is a comrade, who continuously fights alongside with me. Her love, effort, and sacrifices are most deeply appreciated. v ABSTRACT Discrete solid-state high-power amplifiers are among the important circuit components in today’s wireless communications and remote-sensing applications. As the device technologies continue to improve, there are new opportunities and new challenges presented to power amplifier designers. This thesis presents novel techniques in the design and the analysis of L-band high-efficiency power amplifiers, which may be used in many communications and radar applications. In this work, high-efficiency power amplifier topologies are discussed and implemented. The goal is to push the boundary of output power, operating frequency, efficiency and bandwidth. Also, the design of a key passive component, a balanced-to-unbalanced transformer (balun) is discussed in detail. Some new designs of the baluns are shown, and the results show advantages of these baluns over some of the traditional work at L-band. The stability analysis of power amplifiers is one of the most critical and the most challenging aspects of power amplifier design. This work shows an analysis technique, which accurately predicts the oscillations in power amplifiers. Using the technique, different stabilization techniques and circuits are designed and implemented. vi TABLE OF CONTENTS Acknowledgements...................................................................................................................................... iii Abstract..........................................................................................................................................................v Table of Contents .........................................................................................................................................vi List of Figures ............................................................................................................................................ viii List of Tables.................................................................................................................................................xi Chapter 1 Applications of High-Efficiency L-Band Amplifiers ................................................................1 1.1 Cellular Applications ........................................................................................................................2 1.2 Radar Applications............................................................................................................................3 1.3 Organization of Thesis ......................................................................................................................4 Chapter 2 High-Efficiency Design Techniques...........................................................................................6 2.1 Transconductance Amplifiers ...........................................................................................................8 2.1.1 Class-A Amplifiers..................................................................................................................9 2.1.2 Class-AB, Class-B, and Class-C Amplifiers .........................................................................10 2.2 Switching Amplifiers ......................................................................................................................11 2.2.1 Class-D and Class-D-1 Amplifiers .........................................................................................13 2.2.2 Class-E Amplifiers ................................................................................................................15 2.2.3 Class-F and Class-F-1 Amplifiers...........................................................................................16 2.2.4 Class-E/F Family ...................................................................................................................17 2.3 L-Band Implementation of Class-E/F Amplifiers ...........................................................................19 2.3.1 Transistor Output Capacitance and the Second Harmonic Trap............................................19 2.3.2 Loss Mechanisms in Power Amplifiers .................................................................................21 Chapter 3 Transformers, Baluns, and Power-Combining Technologies................................................22 3.1 Baluns in Power Amplifiers ............................................................................................................22 3.2 Examples of Transformers and Baluns ...........................................................................................26 3.2.1 HF, VHF, and UHF Transformers.........................................................................................26 3.2.2 Microwave Baluns and Transformers....................................................................................28 3.2.3 Distributed Active Transformer (DAT).................................................................................29 3.3 Compact L-Band Baluns.................................................................................................................30 3.3.1 Lumped-Element Model........................................................................................................31 3.3.2 Tight-Coupling Microstrip Lines...........................................................................................32 3.3.3 Balance Optimization ............................................................................................................34 3.3.4 Input Impedance Transformation ..........................................................................................36 3.3.5 Output Impedance Transformation........................................................................................38 3.3.6 Center-Tapped DC Feed and 2nd Harmonic Trap.................................................................40 3.4 Balun Selection ...............................................................................................................................44 3.4.1 Bandwidth .............................................................................................................................44 3.4.2 Size ........................................................................................................................................45 3.4.3 Impedance Level and Impedance Transformation.................................................................46 Chapter 4 Implementation of Power Amplifiers ......................................................................................47 4.1 Implementation and Measurement ..................................................................................................48 4.1.1 800 MHz Power Amplifier Using Interdigitated Baluns .......................................................48 4.1.2 900 MHz PA Using Interdigitated Baluns.............................................................................50 4.1.3 1200 MHz PA Using Broadside-Coupling Baluns on FR4 ...................................................52 4.1.4 1100 MHz PA Using Broadside-Coupled Baluns on Duroid ................................................56 4.1.5 1200 MHz PA Using Broadside-Coupled Baluns on Duroid ................................................60 4.2 Performance Comparison................................................................................................................61 ..87 5............102 6.........................................................3 Stabilization with Feedback Resistors ............................................................................3...........1................................................................83 5............................79 5..................65 5....................................................................................................93 6...........................................................................................89 5.................................3 Application to L-Band Power Amplifier..........90 5....3 SiC Class-E Power Amplifier..........100 6...............64 5........78 5...............................4........63 5.............................................................................1............................................2 Determination of Stability Contour ........1 Introduction to Stability Analysis .................................1 Challenges in Discrete L-band DAT ..........................................................................................1 Oscillation Detection Using Small-Signal Generator ..............4 Stabilization Techniques ...................................................................84 5..............................................................................................1 Stabilization with an Odd-Mode Stabilization Resistor.....................................................................103 References ..........3 Bifurcation Analysis Using Auxiliary Generator ............................................................................................................2....................................2 Layout and Simulation .................................................................................2...70 5..98 6..................................................104 ....................................5 Summary ...................4......................3....................................................3 Discrete L-Band DAT.......................................................2 Stabilization with Neutralization Capacitors .............................................................................2.......102 6.......1 New Transistor Technologies .1...................................2 Nonlinear Bifurcation Analysis.............................................................................................vii Chapter 5 Bifurcation Stability Analysis of L-Band Power Amplifier.....................................92 Chapter 6 Future Opportunities ..................................................................................................................................................94 6.........................71 5.................1 Methods in Stability Analysis....................93 6............................................................................2 SiC and GaN Devices...................................................4 Comparison of Performance.....95 6..............2 Modeling for Switching-Mode Amplifiers ........................4...........................................77 5............................................................1 Si and GaAs Devices ................4.1..... ........... .......... Amplitude and phase differences for different load resistances and dielectric constants.......28 Figure 3......................................17 Figure 2. Class-AB....11............4....... Optimization goal for power amplifier’s output balun............20 Figure 2............................42 ...................... Microstrip implementation of Marchand balun..............................15........... Schematic of the output circuit of a power amplifier with a Distributed Active Transformer........................ Voltage and current waveforms of Class-D and Class-D-1 amplifiers.......................... The circuit schematics of Class-F (top) and Class-F-1 (bottom) amplifiers.............................10............. Simulated coupling coefficient of ideal interdigitated inductors.................................... Simplified schematic of a 4:1 Guanella balun.................................14...................... Class-A voltage and current waveforms...................2...... The change of current waveform due to the change in output capacitance................................7..........................9................................................12 Figure 2...........20 Figure 2. Figure 1....... ........15 Figure 2.....31 Figure 3...................... A schematic of push-pull Class-E/Fodd amplifier....6........ A compact magnetic-coupled 50 Ω balun built on FR4 board............................... ...........................................5.................................. A coil transformer using a ferrite core (left)..... Schematic of hybrid-ring balun.......1............. The linearity-efficiency tradeoff between transconductance and switching-mode amplifiers.8............. ..........23.......................................11 Figure 2..................................... . .............. .....................18............. .... .........................................................................33 Figure 3..5 Ω to 50 Ω balun with a 3rd-order band-pass filter......5.............. ...........33 Figure 3................ Current waveform of Class-E/Fodd and Class-E/Fodd.38 Figure 3.....26 Figure 3...................34 Figure 3................................ ............................. Circuit schematic of a Class-E amplifier......................................................................36 Figure 3........... ..........27 Figure 3..... Figure 2.... Quarter-wave coaxial transmission line balun................. .............. The equivalent circuit model of a center-tapped coil transformer balun (right)................9...... Simulation of the 2nd harmonic trap showing an open circuit for the 2nd harmonic.. Schematic of center-tapped DC bias line.......13......................................... ........41 Figure 3............8....... Sample voltage and current waveforms for an ideal switching-mode amplifier..... Impedance matching using the gate capacitance of the transistor and the leakage inductance of the balun......3.........13 Figure 2....................21 Chapter 3... Simulated results for a 7.............. and Class-C amplifiers........ Simple circuit diagram of Class-A.2 amplifiers in the case of large output capacitance in the transistors..............13.............................................................25.............12............................... Broadside coupling balun with coupled inductors in a multilayered board.................. Schematics of Class-D (left) and Class-D-1 (right) amplifiers. ............ A schematic of push-pull Class-E/Fodd amplifier also tuned at an even harmonics..................... Simulated coupling coefficient of ideal broadside-coupling inductors.............................3...........41 Figure 3...14........ Class-AB voltage and current waveforms....29 Figure 3.....16...........19... ... A four-port equivalent circuit model for coupled microstrip lines.7 Figure 2.........................................38 Figure 3................................................................................ .......4...................11 Figure 2.. ...........11........22.9 Figure 2....19 Figure 2...................... ...viii LIST OF FIGURES Chapter 1...40 Figure 3...28 Figure 3.35 Figure 3.......................... A typical push-pull power amplifier topology....... ...........................................8 Figure 2............ Class-C voltage and current waveforms...... A simplified output transistor and balun model for the output balun analysis. ..............1........6............................2.1 Chapter 2........7...........32 Figure 3..................... Input matching optimization for the input balun.............................................. Applications of power amplifiers in low microwave frequency........... Figure 3....29 Figure 3..............39 Figure 3....24...........30 Figure 3................. Comparison between a balun with 50 Ω terminations at all ports and a balun with 50 Ω termination at unbalanced port and 25 Ω terminations at balanced ports............14 Figure 2.........24 Figure 3....................10.............23 Figure 3..............31 Figure 3.......... A compact side-coupled microstrip balun on a dielectric substrate. A half circuit of the transistor and the balun...... Interdigitated balun with coupled inductors connected by wire bonds................10 Figure 2..........................34 Figure 3......................20........................15.....12... Coupled inductors with one port grounded showing asymmetry.................................... Class-B............ Class-B voltage and current waveforms...........21...26.....17................1..........................25 Figure 3........................... Schematic of 2nd harmonic trap on the DC bias line............................... ................ Power amplifier operating in an unstable condition... Photo of the center-tapped input balun......27.72 Figure 5.................................6............5.............. In the plane defined by fin and Pin... Poles and zeros of an L-band power amplifier operating in a stable condition..59 Figure 4....4.....56 Figure 4............... frequency......48 Figure 4..... Input matching network of the L-band power amplifier.14.........2................................................. The vias are shown in red............................12.......... Power amplifier operating in a stable condition... Cross-sectional view of the multilayer PCB built on FR4................... Output power spectrum.............. ................61 Chapter 5...... and the solid lines are measured results................... .......... frequency........................ .............................................12..57 Figure 4................44 Chapter 4................... A typical measurement setup for the power amplifier. .... Measured eye-diagram and phase trellis using an MSK signal....................................................................43 Figure 3............................17....... As the drain voltage increases........ The simulated efficiency improves by 5%........83 Figure 5......... Figure 5.................55 Figure 4...............................4........................................................................ 900 MHz Class-E/F power amplifier with interdigitated baluns........ Gain and PAE vs.................2.......18.............. the low frequency oscillation is observed when drain bias is at 4......76 Figure 5............................... The boundaries between the stable and unstable regions based on global-stability analysis of the amplifier......................21...........................19.. Lines indicate simulation results...................56 Figure 4...............9........................... output power for 800 MHz PA......7........82 Figure 5............. 800 MHz Class-E/F power amplifier with interdigitated baluns....................58 Figure 4................9..............54 Figure 4.............8.................49 Figure 4...................................... Admittance plots showing unstable conditions of the amplifier....................................... The primary inductor in the second layer is directly below the secondary inductor.................. Simulated output spectrum without (top) and with (bottom) the second harmonic tank......................................60 Figure 4... Schematic of stabilization circuit using odd-mode stabilization resistor... frequency......... ........ Simulated waveform of Class-E/F amplifier.85 ........75 Figure 5................................ gain and PAE vs.............. ....... Gain and input return loss vs.............................6................................... Gain and PAE vs.................... Lines indicate simulation results.........1................................. Gain and efficiency vs..................60 Figure 4.........................80 Figure 5.............. Output power and return loss vs... output Power at 1075 MHz... The boundaries between the stable and unstable regions based on global-stability analysis of the amplifier..............53 Figure 4............ Gain and PAE vs........ Cross-sectional view of the multilayer PCB built on FR4.10............. ... . In the plane defined by VG and VD............. .... frequency demonstrate the use of Kurokawa’s condition to determine the stability conditions....................................8.........81 Figure 5......... Output power............................13.... Plots of the real and imaginary parts of the admittance function vs...........3................. ......7.......................5....................... Figure 4......... Conversion matrix approach to detect oscillations using a small-signal current source inserted at one node of the power amplifier..............59 Figure 4............ Layout of 1200 MHz Class-E/F power amplifier with broadside-coupling baluns. Poles and zeros of an L-band power amplifier operating in an unstable condition....... Oscillations in L-band power amplifier. Admittance plots showing stable conditions of the amplifier.............22...50 Figure 4..................................55 Figure 4...... .. ................ Plot of the real and imaginary parts of the admittance function vs....79 Figure 5...........54 Figure 4...... Simplified schematic of the Class-E/Fodd.........................2 amplifier... Schematic of auxiliary generator applied to a power amplifier..... and markers indicate measurement points.... .11... 1200 MHz Class-E/F power amplifier with broadside-coupling baluns on Duroid................................. Block diagram of the measurement setup.......13.................................3.....16.................. The oscillation is drive frequency is 1030 MHz........... ..................... output power. ................................... for different operation conditions........11............... output power at 1220 MHz......1.... for different operation conditions.......... The dash lines are simulated results..........20......................................ix Figure 3.............52 Figure 4................. .....................74 Figure 5.................................. ...................................................... ........... The switching voltage and current waveforms........ frequency demonstrate the use of Kurokawa’s condition to determine the stability conditions...........57 Figure 4.............. The oscillation occurs at about 200 MHz........................ 1200 MHz Class-E/F power amplifier with broadside-coupling baluns on FR4........ and markers indicate measurement points.....15......77 Figure 5.......................49 Figure 4............58 Figure 4.......... ................28............................................................................51 Figure 4.. with the input power and gate bias voltage fixed..................................5 V...............10.............77 Figure 5........................... Frequency spectrum of fundamental and harmonics......76 Figure 5...... .. Simplified switch model for the input and the output circuit of the transistor............89 Figure 5..6....18...................... For clarity reasons............. only a portion of the representative curves are shown..... Stabilization with an odd-mode stabilization resistor............................................................. ....... only two representative sets of curves are shown.. Layout of SiC Class-E power amplifier ................... ................14........................................................................................... Stabilization circuit using feedback resistors and DC-blocking capacitors.............16.....................88 Figure 5...................7.... Typical operation conditions have been considered in these simulations............. Schematic of stabilization circuit using neutralization capacitors............. Photos of two 10W L-band power transistors: Freescale MRF282S Si LDMOS (left) and Cree CRF 24010 SiC MESFET (right).................................................... ................ Switch model of the transistor output circuit......86 Figure 5......... For clarity purposes................90 Figure 5... ................................................................................... Measured amplifier performance before and after applying odd-mode stabilization resistor of 150 Ω.......17....... Measured input and output impedance of the SiC MESFET.........5..19................... Photo of Class-E SiC power amplifier.........96 Figure 6.20.........98 Figure 6....................8..99 Figure 6.............. Admittance plot for various stabilization resistances.......................87 Figure 5..................................... Measurement bandwidth performance of the SiC power amplifier............................................ Figure 6.....99 Figure 6.................97 Figure 6...........101 Figure 6..............4........103 ............... Simulated amplifier performance after applying three different stabilization techniques.. Typical operation conditions have been considered in these simulations..x Figure 5............................90 Figure 5.........................21.................................... ......... ................ .......................................................3................................................................................2... Output circuit of the PA with DAT and an external output tuning capacitor.............1.........91 Chapter 6...................15...........................91 Figure 5............... ........................101 Figure 6...... Stabilization with feedback resistors...................................... ..................... Stabilization with neutralization capacitors using bifurcation loci.. ..........................................................................................................2 Specifications of Freescale MRF 284................3 The phases of voltages at the gate and drain terminals..74 Table 5..............62 Table 5..........xi LIST OF TABLES Table 2..........................1...........................4 Comparison of Performance with Published Results ....93 Table 6.........................................47 Table 4..............................................75 Table 5....47 Table 4.........................84 Table 6...................61 Table 4.............................1 Amplifier Specifications................................1... Harmonic Terminations of Different Classes of Power Amplifiers ........ Poles and Zeros of an L-Band Power Amplifier in an Unstable Condition......18 Table 4................................................................................ Comparison of Key Specifications of LDMOS and SiC Devices .................................3 Performance Summary of Different Versions of Amplifiers...2....................1. Poles and Zeros of an L-Band Power Amplifier in a Stable Condition. Key Properties Comparison for Microwave Power Transistors .................................................................96 .2....... are also emerging and high power amplifiers are needed in the hundred watt level beyond 2. Applications of power amplifiers in low microwave frequency.1 shows only some of the main applications in this frequency band. This opens up possibilities to achieve wireless communications for longer range and for better quality. lower microwave frequency. Newer applications. As the technology pushes for higher output power at higher operating frequency. In today’s technology.1 Chapter 1 Applications of High-Efficiency L-Band Amplifiers The growth in wireless communications and radar applications has put greater demand on the performance of power amplifiers (PAs). a commercially available package of a push-pull pair of two transistors can output over 200 W at 2 GHz for base station applications [1][2][3]. such as WiMax. we Future Applications GSM Basestation GSM and CDMA Basestation L-Band Remote Sensing Avionics WiMax . WCDMA Basestation Figure 1.1. One of the fundamental problems in today’s wireless technologies is the limitation of energy resource.5 GHz. For cellular handsets. In the recent years. has dominated the commercial wireless market. The rapid growth in device technologies and processing technologies presents new opportunities to power amplifier designers.5 GHz. from 800 MHz to 2. there are also many challenges presented to PA designers. Figure 1. Since the amplifiers discussed in the dissertation are used for remote-sensing applications. power amplifiers are the most power-consuming components. The cellular phone market has grown tremendously over the past decade. the emphasis will be on L-band radar applications. The efficiency of the power amplifier directly determines the energy consumption of the transceiver. and 2100 MHz. due to their different power level. the most important requirement is linearity.2 want to have high efficiency to conserve battery energy. We will discuss the applications of high-efficiency high-power amplifiers in two areas: cellular base station and remote-sensing radar. and in today’s technology. 1. high-efficiency transmitters can save energy while using wireless internet. Most base station amplifiers are operated in linear or weakly nonlinear mode. In these wireless transceivers. Properly designed high-efficiency amplifiers reduce heat dissipation. The efficiency of these . are beyond the scope of this dissertation. Most of the handset PAs are built on chip as integrated circuits with a few off-chip components. In satellite applications. The handset PAs typically have maximum output power ranges from one watt to a few watts. There are even PAs fully integrated on chip [4][5]. These amplifiers. different processing technology and different set of optimization parameters. 900 MHz. in high power amplifiers. The base station power amplifiers have output power of tens or hundreds of watts.1 Cellular Applications There is no need to emphasize the importance of cellular phones in everyday life today. Cellular applications typically cover several low microwave frequency bands. 1900 MHz. thereby improving the reliability of amplifiers and reducing the need for bulky and heavy heat sinks. they have to be implemented with discrete or hybrid technologies. highefficiency transmitters reduce high energy cost. For wireless communication applications. including 800 MHz. On laptop computers. heat dissipation has become a limiting factor when devices are operating in higher and higher power. This requirement puts constraints on the design of power amplifiers. Furthermore. 1800 MHz. Doherty.3 amplifiers is low compared to an amplifier driven well into saturation. The dynamics of the solid Earth motion are complex and there are vigorous efforts to model. land cover change). which could have dual-use science and military application. For example. understand and eventually predict earthquakes using InSAR data.2 Radar Applications Radar remote sensing plays an important role in deriving unique measurements that address fundamental questions in the National Aeronautic and Space Administration (NASA) Earth Science Enterprise (ESE) strategic plan. L-band SAR can provide information on vehicle and troop movements. such as the measurement of surface soil moisture and sub-pixel roughness for trafficability. Synthetic aperture radar (SAR) can provide measurements key to the water cycle (e. with wide coverage at fine resolution and with minimal temporal decorrelation [6][7]. L-band radar technologies could also have application to future DoD space-based radar (SBR) for airborne moving target indication (AMTI) and ground moving target indication (GMTI). soil moisture and water level). L-band repeat-pass interferometric SAR (InSAR) techniques can provide very accurate and systematic measurements of surface deformation and surface strain accumulation due to seismic and volcanic activity. However. and ocean circulation and ice mass (ice motion). envelope tracking.g. and building damage. day or night. L-band InSAR is also useful for natural hazard monitoring. and several digital pre-distortion methods have shown promises to use strongly nonlinear amplifiers to be used in linear wireless applications such as EDGE and WCDMA. assessment and disaster response. Furthermore. . 1. Significant contributions are also possible in providing detailed surface characteristics. global ecosystem (biomass estimation. L-band radar provides the ability to make these measurements under a variety of topographic and land cover conditions. these techniques could provide observations that are complementary to the traditional high-resolution imagery of the intelligence community. in the recent years. L-band SAR technologies developed for NASA also have national security application. 4 1. VHF and UHF frequencies to microwave frequencies. The chapter focuses on the techniques and circuit topologies that improve the efficiency of power amplifiers. Chapter 5 discusses one of the important aspects of power amplifier design: stability analysis. The chapters are organized as followings: Chapter 2 reviews some of the most typical classes of power amplifiers.3 Organization of Thesis This thesis focuses on the design and implementation of L-band compact. Chapter 6 leads to the future work of L-band power amplifier design. Several different stabilization techniques are discussed and compared. In particular. The chapter describes the limitations of the current stability analysis techniques. It introduces a series of techniques based on the nonlinear bifurcation analysis. The implementations of these techniques in L-band are presented. The analysis includes oscillation detection and pole-zero analysis. Preliminary results using SiC transistors are presented. Chapter 4 presents the simulated and measured results of several different versions of amplifiers. Chapter 3 discusses a key component of the amplifier: balanced-to-unbalanced transformers or baluns. current and new transistor technologies are reviewed. The use of these classes in high-power and high-efficiency application at UHF and low microwave frequency bands are discussed. and the balun has good performance along with important features such as impedance-transformation and harmonic tuning. In order to properly use the newer . Conversion matrix technique and auxiliary generator technique are also presented. The chapter demonstrates the improvements in iterations of amplifiers. SiC and GaN devices are introduced. A novel balun is presented. The final results are compared with the state-of-the-art amplifiers. and the performance is shown. These amplifiers are used in the L-band radar T/R modules described above. The power amplifier is stabilized. Different balun topologies are presented from HF. high-efficiency power amplifiers. Feiyu Wang. Tech. vol. Conf. Oct. Rutledge. Maryland. 10. Edelstein. Rutledge. David B. Alina Moussessian. “Current status of the high-efficiency L-band transmit/receive module Development for SAR Systems. Feiyu Wang and David B. There are discussions on the limitations of the current modeling approaches and newer approaches in modeling active devices..” Proc. 2004. Edelstein. the chapter discusses the possible implementation of discrete Distributed Active Transformer in L-band to improve the output power. 2005. “Bifurcation analysis of stabilization circuits in an L-band LDMOS 60-W power amplifier. Dig. Adelphi. Wendy N. no. improvement in the area of device modeling has to be made. Conf.2 LDMOS power amplifier using compact multilayered baluns. “High-efficiency L-band transmit/receive module for synthetic aperture radar. David B. . Maryland. 238–243. Constantine Andricos.” IEEE Topical Workshop on Power Amplifiers for Wireless Comm. Constantine Andricos.” IEEE Microwave Wireless Compon. Wendy N. Edelstein. David B. pp. Rutledge. Soren Madson. 2003. “A 60-W L-Band Class-E/Fodd. 712–714. Tech. May. Wendy N. 15. This dissertation is based on the following published work: Feiyu Wang. Lett. Adelphi..5 device technologies. Rutledge.. Rutledge.. Finally. Sep. Feiyu Wang.” NASA 2003 Earth-Sun Syst. pp. Feiyu Wang. Tech. Almudena Suarez. 2003 IEEE Radar Conf... “Highefficiency L-band T/R module: development results. Constantine Andricos.” NASA 2005 Earth-Sun Syst. David B. and Class-F amplifiers. some classes can be thought of as a limiting case of other amplifiers. Class-B. These classes are typically denoted as “Class-XY” amplifiers. and linearity vs.6 Chapter 2 High-Efficiency Design Techniques Power amplifiers are widely used in wireless communication applications and radar applications. Conventional switching-mode amplifiers include Class-D. Another class of amplifiers combines the advantages of Class-E and Class-F-1 . It is worth noting that there are a lot of confusion and debates over the classification of power amplifiers. bandwidth. and cost. efficiency. and only a subset of the requirements can be satisfied. power amplifiers are divided into two types: transconductance amplifiers and switching-mode amplifiers. Class-AB. Several classes of amplifiers attempt to combine advantages of two different classes. Some of the classic tradeoffs include: gain vs. there is a great variety of requirements for power amplifiers. Some examples of these intermediate classes of amplifiers include: Class-BD [8]. Some classes overlap others. Class-E. Nevertheless. and Class-C amplifiers. While some classes of amplifiers have advantages over other classes. they also have disadvantages. Thereby tradeoffs must be made. It is almost never possible to simultaneously maximize all design criteria at the same time. As knowledge of power amplifiers accumulates. efficiency. output power. linearity. gain. size. many different classes of power amplifiers have evolved over the years. Each of the power amplifier classes optimizes a certain subset of design criteria. Due to the variety of applications. Class-CE [9]. operating frequency vs. A typical attempt to optimize a subset of design criteria is the introduction of different classes of power amplifiers. bandwidth. Some of the most basic requirements in power amplifier design include frequency of operation. output power level. Conventional transconductance amplifiers include Class-A. Generally speaking. the current classification gives a good starting point for basic understanding of these amplifiers. and Class-DE [10]. The linearity-efficiency tradeoff between transconductance amplifiers and switching-mode amplifiers.1 and use a Class-A or a Class-AB amplifier as the starting point. and it is called the Class-E/F amplifiers. Switching-mode amplifiers can achieve an ideal efficiency of 100%. Class-AB. .7 amplifiers. we will only focus on the techniques that improve the efficiency of the amplifiers. The problem is that many applications require that high linearity and high efficiency be achieved at the same time.or post-distortion techniques [21][22][23].1. These techniques include Envelope Elimination and Restoration (EER) technique [12][13][14][15]. Chireix [18][19][20] and even digital pre. These techniques are beyond the scope of the thesis. and then investigate complicated linearization techniques. Naturally. but they are strongly nonlinear amplifiers.1. Doherty [16][17]. This particular class was invented by Scott Kee at Caltech [11]. The classic tradeoff between the transconductance amplifiers and switching-mode amplifiers are linearity and efficiency. Class-B. they can achieve a maximum efficiency of 50%. While Class-A amplifiers are the most linear power amplifiers. some PA designers choose to start from the left side of Figure 2. Some other PA designers choose to start from a switching-mode topology of the amplifier with high efficiency. and Class-C amplifiers are compromises in between as shown in Figure 2. Linearity Efficiency Transconductance Amplifiers Switching Amplifiers Class D / D-1 Class E Class F / F-1 Class E/F Class A Class AB Class B Class C Figure 2. and then try to find a solution to improve efficiency without compromising the linearity. Since the power amplifiers described in the thesis will be used in applications where highly nonlinear effects can be tolerated. Class-B. The circuit is single ended. Figure 2.8 Two of the most noteworthy schools of high-efficiency PA design are: (1) voltage and current waveform shaping using time-domain techniques. In this chapter. Discussions emphasize on high-efficiency design techniques used in switching-mode amplifiers. DC-coupling capacitor and the filter are all ideal. Class-C amplifiers. Class-A. It is important to look beyond the class nomenclature. These amplifiers use active transistors as controlled current sources. Class-AB. and Class-C amplifiers. and Class-C amplifiers are conventional transconductance amplifiers. (2) voltage and current waveform shaping using frequency-domain or harmonic-tuning techniques as in Class-F amplifiers. Figure 2. and they have been discussed in detail in several books [24][25][26]. several typical classes of power amplifiers are reviewed. In this thesis. Class-B. Class-B. only common-source or common-emitter configurations are considered.2.1 Transconductance Amplifiers Transconductance power amplifiers are extensions from linear transconductance amplifiers. Class-AB. 2. . and we assume that the RF choke. as in Class-E amplifiers. and often it is easier to understand the newer techniques based on these two theories. Simple circuit diagram of Class-A.2 shows a simplest circuit diagram of Class-A. They are widely used in today’s wireless transmitters. Class-AB. 5 Figure 2.1 Class-A Amplifiers The most simplistic way to distinguish these classical transconductance amplifiers is the conduction angle.5 0 Voltage 1. the biggest drawback of the Class-A amplifier is the ideal maximum efficiency of 50%.5 Time 1 1. the use of Class-A amplifiers is only popular at high microwave frequency beyond 5 GHz up to millimeter-wave territory. Class-A voltage and current waveforms. .9 2. In today’s technology. Class-A is much more suitable. The Class-A amplifier is the most linear and the most “well-behaved” amplifier. Class-AB amplifiers have a conduction angle of π < θ C < 2π .3 shows the voltage and waveforms of a Class-A amplifier.3. the total power consumption of the power amplifier is 300 W.5 0 0 0. is reduced significantly to about 35% for Lband applications.5 2 1 0. Since at higher frequency. in practice. the power gain is usually the limiting factor in PA design. Figure 2. Class-B amplifiers have a conduction angle of π . However. 2 Current 1. If the output power of the amplifier is 100 W. This number is usually well beyond the heat-handling capability of a common-source transistor package. Let us take 33% drain efficiency as an example. This is the reason why Class-A amplifiers are not suitable for L-band high-power amplifiers.5 1 0. Class-C amplifiers have a conduction angle of 0 < θ C < π . and 200 W is dissipated power. Class-A amplifiers have a conduction angle of θ C = 2π .1. The advantage of the Class-A amplifier at higher frequency range is that it requires considerably less drive power and has higher gain than other classes of power amplifiers. This efficiency number. 10 2. Since the gate bias level is reduced from Class-A amplifier.5 1 0.5 0 0 0. Class-B. which is significantly higher than the Class-A amplifier. Class-AB voltage and current waveforms.2 Class-AB. 2 Current 1.4.4. and apply harmonic control techniques to improve efficiency. Class-AB amplifiers are popular candidates for L-band power amplifiers.1.5 0 Voltage 1. We can look at a Class-B amplifier as a transition between a Class-AB and a Class-C amplifier. an L-band high-power Class-B amplifier can achieve a drain efficiency of 60%. the current clipping occurs. These techniques are discussed in the later part of the chapter. We can easily see that is a great reduction from 200W in the Class-A case. If we take the same case as before. . Although current clipping generates harmonics and nonlinear effects. The ideal maximum drain efficiency of a Class-B amplifier is 78. Higher efficiency than Class-A amplifiers can be obtained without much compromise in the power gain and the linearity.5 Time 1 1. we see that for an output power of 100W. and Class-C Amplifiers The voltage and the current waveforms of a Class-AB amplifier are shown in Figure 2.5%.5 2 1 0. a practical Class-B amplifier only dissipates about 60W of power. Practically.5 Figure 2. Many PA designers use Class-AB amplifiers as a starting point. The first drawback of this amplifier is the efficiency comes at the expense of the power gain.5 1 0. the active device is ideally fully on (short-circuit) or fully off (open-circuit). 2. the output power approaches to zero.5 2 1. as the efficiency approaches to 100%. in the classic definition of Class-C amplifier.5 1 0. with an ideal efficiency of 100%. this approach is typically not desired. However.5 1 0.5 0 Figure 2. Class-B voltage and current waveforms. At microwave frequency. That is. or it has to be used with linearization techniques.5 0 Voltage Voltage 1. so it can be used only in applications that can tolerate a high degree of nonlinearity.5 2 1 0.2 Switching Amplifiers Switching-mode power amplifiers use active transistors as switches. 2 Current 1.5. The second drawback is that the amplifier is highly nonlinear.5 0 0 0. since high power gain is difficult to obtain. Class-C amplifiers are high-efficiency amplifiers. These circuits are commonly found in switching power supplies.5 Time 1 1.5 Time 1 1.11 2 Current 1.5 0 0 0. there are several problems for an L-band Class-C implementation.5 Figure 2.6. In fact. but only recently have they been exploited . Class-C voltage and current waveforms. 2 Current 1.7. we will start from one of the simpler approaches of switching-mode amplifiers: Class-D and Class-D-1 amplifiers.5 0 0 0. To see how to achieve no overlapping between the voltage and the current.12 as RF amplifiers due to the availability of transistors with substantial gain and power at microwave frequencies. which use the active devices as controlled current sources. Class-C amplifier has the highest efficiency due to the least overlap between nonzero voltage and current region. In ideal switching-mode amplifiers. This theoretical number is significantly higher than the traditional Class-A and Class-AB amplifiers. The switching-mode amplifiers differ from the traditional classes of amplifiers. ideally no power is dissipated. Note that the current and the voltage do not overlap. Since ideally the device is either fully on or fully off. we see that from the transconductance amplifiers already. the transition between the on-state and the off-state can be achieved instantaneously. we see that in Class-A amplifier. we need to reduce the overlap between the voltage and the current. If we compare the voltage and the current waveforms from the four different transconductance classes discussed in the previous section.5 Time 1 1. To optimize the efficiency. the current and the voltage are both non-zero at all time. In fact. and the efficiency is 100%. . and the Class-A amplifier has the lowest efficiency.5 0 Voltage 1.5 1 0.7. practical efficiencies of 70-90% have been demonstrated at VHF and UHF frequencies [27][28][29]. The theoretical efficiency for Class-E and Class-E/F amplifiers is 100%. Therefore.5 Figure 2.5 ON OFF 2 1 0. the voltage and the current will never be nonzero simultaneously as shown in Figure 2. Sample voltage and current waveforms for an ideal switching-mode amplifier. and the voltage waveform is sinusoidal. Class-D-1 amplifier’s band-pass filter has an open circuit at the fundamental frequency and a short circuit at other frequencies. The current waveform is a square wave. Schematics of Class-D (left) and Class-D-1 (right) amplifiers.1 Class-D and Class-D-1 Amplifiers Class-D and Class-D-1 (also called inverse Class-D or current-mode Class-D) amplifiers use two active devices driven as switches at 180o out of phase (in a push-pull configuration). . The load circuit consists of a band-pass or a band-stop filter. RLoad RLoad Short at f = fin Open otherwise Open at f = fin Short otherwise Vd1 Vdd Vd2 Vd1 Vdd Vd2 Vg1 Vg2 Vg1 Vg2 Figure 2.9. The waveforms of Class-D and Class-D-1 are shown in Figure 2. while the current waveform is sinusoidal. The voltage waveform is a square wave.13 2.2. Class-D amplifier’s band-pass filter has a short circuit at the fundamental frequency and an open circuit at other frequencies.8. If this capacitance is not too large. It is also assumed that in Class-D and Class-D-1 amplifiers. the devices are typically large in size. which can be toggled between ON state and OFF state instantaneously. In high-power amplifiers. This drawback is addressed in the time-domain design and analysis in Class-E amplifiers.5 ON 1 Time Figure 2.5 Time 1 1.8. This is commonly referred as the output capacitance is “absorbed” in the tuning circuit. We will discuss this point further in the later sections. However. the effect by the output capacitance cannot be ignored. so at UHF and microwave frequencies. we see that the output capacitances of the devices are in parallel with the parallel resonance circuit. we can in fact use this capacitance as a part of the parallel resonance circuit.9. Therefore. Under ideal conditions. Class-D and Class-D-1 can achieve 100% efficiency. and thereby having a large output capacitance. The susceptance of the output capacitance also increases with frequency. the transistors behave as switches. one of the assumptions of Class-D and Class-D-1 amplifiers is that the transistors have zero output capacitance. and increase the transistor loss. the effect of the output capacitance is not the same. Voltage and current waveforms of Class-D and Class-D-1 amplifiers. we can still achieve ideal efficiency of 100%. . thereby the use of this type of power amplifiers are mostly limited to audio amplifiers.14 4 Current 3 2 1 0 0 ON Class D 4 Voltage 2 Current 4 3 2 1 0 0 Class D-1 4 Voltage 3 2 1 0 1. the voltage and the current waveforms overlap. the loss due to large output capacitance can be very large in microwave frequency. In Class-D-1 amplifier. If we look carefully at the schematic in Figure 2.5 OFF OFF 0. This is certainly not the case in microwave transistors.5 3 1 0 0. In Class-D configuration. Within the finite turn-on and turn-off time. Class-E tuning reduces the slope of the voltage waveform before the switch turns on. This basic circuit is shown in Figure 2. Also. At microwave frequency. and the loss may be too great to tolerate. a Class-D amplifier suffers power loss due to the voltage and the current are simultaneously nonzero. Since the switching time of the transistors is not instantaneous.2. Vdd Lchoke Vd Short at f = fin Open otherwise Vg Rload Figure 2. This feature. Sokal [30][31]. Circuit schematic of a Class-E amplifier. Another beauty of Class-E amplifier is the relatively simple circuit topology for an easy implementation.2 Class-E Amplifiers The Class-E amplifiers were invented by N. which assume a zero output capacitance . minimizes the level of the voltage during the turn-on of the switch. From the time-domain waveform of the voltage. Sokal and A. D. The main advantages of Class-E amplifiers are: (1) “soft-switching” to reduce loss.15 2. sometimes referred to as soft-switching or zero-voltage-derivativeswitching (ZdVS). (3) relatively simple circuit compared to Class-F amplifier. (2) “absorption of output capacitor” in the output circuit. the switching time may be a significant fraction of the cycle. The ClassE amplifier consists of a single-ended transistor as a switch with an output load circuit. unlike Class-D amplifiers.10. This adverse effect can be significantly reduced in Class-E tuning. The output load circuit has a series resonant circuit at the fundamental frequency along with load impedance which is tuned slightly inductive. O.10. when the inventors include an inductive load. and in turn improves the efficiency.11. To the first order. . The amplifiers achieve high efficiency by shaping the drain voltage or drain current waveforms using these harmonic open or short circuits shown in Figure 2. The current waveform has a lower rms value. Also the efficiency of the amplifier reduces significantly as the output capacitance of the transistor becomes large.3 Class-F and Class-F-1 Amplifiers Class F and Class-F-1 are power amplifiers based on waveform shaping using multiple harmonic resonators.2. and the switch is terminated with a virtual open circuit for even harmonics. The ideal waveforms of a Class-F and Class-F-1 amplifier are very similar to those of a Class-D and Class-D-1 amplifier shown in Figure 2. so the amplifier can be operated in a higher bias voltage without exceeding the breakdown voltage of the transistor. We can look at Class-D-1 amplifiers as a special implementation of the Class-F-1 amplifiers. which reduces the resistive loss of the transistor. The reason for this similarity is symmetric topology of Class-D-1 design. This causes undesired effects. The Class-E amplifier is not quite the perfect solution for high-efficiency PA.9. In this case. In practice. If we take the Class-F-1 as an example. the even harmonics are being terminated with the output capacitance. The amplifier suffers from relatively high peak voltage and high rms current compared to the ideal ClassD-1 amplifier. the output capacitance of the transistor cannot be omitted. it has low peak voltage. At the line of symmetry. which will be discussed in the next section. the switch is terminated with virtual short circuits for odd harmonics. This improves the output power level of the amplifier. 2.16 of the active device. this is a frequency-domain technique compared to the time-domain technique of Class-E amplifiers. Class-E amplifier design equations take into account the output capacitance. In practice. The switch is terminated like the Class-F-1 amplifiers.17 Vdd Lchoke Vd Open for odd harmonics except the fundamental Vg Open for the fundamental Short for even harmonics Rload Vdd Lchoke Vd Short for odd harmonics Vg Open for the fundamental Open for even harmonics Rload Figure 2. Class-E/F amplifiers combine the advantages of Class-E and Class-F-1 amplifiers.2.11 that the circuit requires infinite number of harmonic-control circuits to achieve the ideal Class-F tuning. A push-pull Class-E/F topology is relatively simple as Class-D-1 and ClassE amplifiers. we can take a close look at the Class-E/F family of power amplifiers. A solution to achieve desired harmonic tuning with simple circuits like Class-D and Class-E amplifiers is in the next section. . The circuit schematics of Class-F (top) and Class-F-1 (bottom) amplifiers. It is also clear from the schematic in Figure 2.4 Class-E/F Family After we have looked carefully at two different waveform shaping techniques through Class-E and Class-F design. which is difficult to implement. it translates into a complex circuit. The load is tuned inductive to achieve soft switching. which was invented by Scott Kee and Ichiro Aoki at Caltech [11][33][34].11. 2. 3 Class E/Fodd Class E/Fodd. Also by symmetry of the push-pull configuration. . the Class-E/F design may also tune critical even harmonics to significantly improve the efficiency of the amplifier. z-th harmonics are denoted as Class-E/Fx. Also by examining the topology carefully. The amplifier uses a pair of transistors as switches. Some of the examples of the notation are shown in Table 2. This reduces the undesired effects of the output capacitance. Overall. y.z amplifier. Table 2. But we will see that in addition to odd harmonic tuning. The transistors are driven 180o out of phase. if the output capacitance of the transistor is low. we can say that the Class-E/Fodd amplifier reduces to a Class-D-1 amplifier. The circuit topology is almost identical to Class-D-1 shown in Figure 2.1. If all the odd harmonics of are terminated with short circuits. the amplifier suppresses the even harmonics of the operating frequency. A Class-E/F amplifier which has a Class-F-1-like terminations at x. thereby achieving higher efficiency.12 shows the schematic of a subset of Class-E/F amplifier—a push-pull ClassE/Fodd power amplifier.2 Figure 2. Harmonic Terminations of Different Classes of Power Amplifiers 2 f0 3 f0 4 f0 5 f0 6 f0 7 f0 8 f0 f0 R+L C C C C C C C R open short open short open Short open R+L open short C C C C C R+L C short C short C Short C R+L open short C short C Short C Class E Class F-1 Class E/F2. we can see that the output capacitance can be used as a part of the resonance circuit between the drains of the transistor.8 with two minor differences: the output capacitances of the transistors are considered. the load is tuned slightly inductive like Class-E amplifier to achieve soft switching.18 To reduce the complexity of the circuit. only selected number of harmonics are controlled like Class-F-1. the notation becomes Class-E/Fodd amplifier.y. The odd harmonics are shorted by the virtual ground at the line of symmetry.1. the output capacitance is the limiting factor of the performance. .13. 2. As the output capacitance increases. the output power is limited.12. The current waveform starts from a square wave in the case of zero output capacitance. the passive elements are lossy and non-ideal. the current waveforms are shown in Figure 2.3 L-Band Implementation of Class-E/F Amplifiers At microwave frequencies. power gain over 10 dB is a luxury. 2. but high-power devices still have large input and output capacitances. If the goal is to increase the output power and the operating frequency while still maintaining high efficiency. If we include the output capacitance in the model.19 RLoad XL Vd1 Open at f = fin Short otherwise Vd2 Vg1 Vg2 Figure 2. The current waveform is not desired because the rms current increases. the bandwidth is limited.1 Transistor Output Capacitance and the Second Harmonic Trap The power transistors in UHF and microwave frequency bands have improved in the past several decades. a sinusoidal component at the fundamental frequency is added to the square wave. A schematic of push-pull Class-E/Fodd amplifier. It is no surprise that for a given transistor technology. Since the classic Class-D-1 amplifier analysis does not take into account the output capacitance. it has ideal voltage and current waveforms. the active transistors are not perfect. we want to push its limit in frequency and output power at the same time.3. The change of current waveform due to the change in output capacitance of the transistors in Class-E/Fodd amplifiers.5 1 0.25 0. The improved current waveform is shown in Figure 2.75 1 4 3 2 1 0 Voltage (normalized) Figure 2. and the efficiency is improved by up to 5%.5 0 0 0.5 Time (normalized) 0.20 Increase Cout 2 Current (normalized) 1. RLoad XL Open at f = fin Short otherwise Vd1 Vdd Vd2 Vg1 -C at desired even harmonics Vg2 Figure 2. .14. the switch is terminated with an open circuit. To achieve better efficiency. Effectively. instead of a capacitive load as shown in Figure 2.13. a second-harmonic trap is introduced.15. A schematic of push-pull Class-E/Fodd amplifier also tuned at an even harmonic or even harmonics.14. Using the harmonic trap. we add a negative capacitance at the second harmonic in parallel with the output capacitance. Due to the topology of the push-pull amplifier. Proper modeling of parasitic capacitance and inductance is also another important challenge to ensure the circuit can be properly designed and reproduced to the given requirements. At L-band.2 Figure 2.25 0.21 Current (normalized) 1.3.75 1 3 2 1 0 Class-E/Fodd. The primary loss mechanisms due to passive structures include metal resistive loss and dielectric loss.5 0 0 0. the high-power active devices are typically large in size. This balun must be small and planar with a flexible geometry for easy integration into the amplifier circuit. and very low input and output impedances. 2. The primary loss mechanisms due to active devices include conduction loss. Class-E and Class-E/F amplifiers minimize this switching loss.5 Time (normalized) 0. large output capacitance.5 1 0. all these factors contribute to the different types of losses. Voltage (normalized) Class-E/Fodd 2 4 .15. discharge loss and matching loss. Active device losses for switch-mode amplifiers occur mainly during transitions from one switch state to another. The design of a low loss passive network also presents technical challenges. A comparison between the current waveform of Class-E/Fodd and ClassE/Fodd.2 amplifiers in the case of large output capacitance in the transistors. a balun is used to convert the single-ended signal to a double-ended signal at the input and vice versa at the output. By using a high-Q resonant output network. These power losses can be divided into losses due to active devices and losses due to passive elements. have large on-resistance.2 Loss Mechanisms in Power Amplifiers The design of high-efficiency microwave power amplifiers requires proper trade-off between different types of power losses. VHF. different baluns are compared in terms of bandwidth. which have very low input and output impedances. Finally. The insertion loss is kept to a minimum. Several new compact and planar baluns are introduced. and the phases of the signals are 180o out of phase. These impedance-transforming circuits need to be low-loss and meet the bandwidth requirement of the application. The balun has three ports. 3. proper impedance transformation to 50Ω connectors is critical in the design of power amplifiers. These baluns are capable of impedance transformation. Since high-power amplifiers require large devices. Both input and output baluns need to achieve the following desired characteristics. HF. which are ideal for power amplifier’s low-impedance environment. and the other two ports are the balanced ports. losses. This comparison provides a guide to select a proper balun structure for a specific application. UHF. or balun. and Power-Combining Technologies In this chapter. such as centered-tapped DC feed and harmonic tuning. impedance and powerhandling capability. Baluns. The new baluns are able to handle high power with low loss.22 Chapter 3 Transformers. and microwave transformers and baluns are reviewed. size. The topology of push-pull amplifiers shown in Chapter 2 requires a special type of balanced-to-unbalanced transformer.1 Baluns in Power Amplifiers Transformers are critical passive components in power amplifiers. One port is the unbalanced port. at the input and output of the amplifier to convert the unbalanced signal to balanced signal and vice versa. The insertion loss may include . Extra features. The balance implies that the magnitudes of the signals are the same. are also included in the baluns. 23 the metal loss, the dielectric loss, and the loss due to other on-board components, such as chip capacitors. A typical block diagram of a discrete L-band push-pull amplifier is shown in Figure 3.1. At the input and the output of the amplifier, there are two 50 Ω stand-alone baluns. These baluns have port impedances of 50 Ω at all three ports. Between the active devices and the baluns, there are input and output matching networks, which typically consist of transmission lines and discrete inductors and capacitors. The DC-bias lines at this frequency also consist of high value discrete inductors, or quarter-wave transmission lines. For high-efficiency applications, there are also harmonic-tuning circuits at the output of the amplifier. Vgg Vdd RF Choke Input Balun Input Matching Harmonic Output Tuning Matching Output Balun RF Input RF Output Figure 3.1. A typical push-pull power amplifier topology. The 50 Ω baluns in the block diagram are easy to measure and useful for a variety of applications. In fact, two identical 50 Ω baluns may be used at the input and the output of the amplifier. However, these baluns are not optimized for the purpose of power amplifiers for several reasons. First, using 50 Ω baluns is not an efficient use of impedance transformation in power amplifiers. It is important to realize that 50 Ω baluns are not 1:1 baluns. Since 50 Ω impedances at the balanced ports are effectively in series, 50 Ω baluns actually transform the impedance from 100 Ω to 50 Ω. That means that we need to up-convert low 24 impedances at the gate and the drain of the transistors to 100 Ω and then down-convert to 50 Ω. This significantly reduces the bandwidth of the amplifier. One obvious improvement to this approach is to design 50 Ω to 25 Ω baluns, which take advantage of the nice feature of push-pull amplifiers that the gates and drains are in series. This is demonstrated in Figure 3.2. But even this approach does not take into account the second disadvantage of this type of balun. Figure 3.2. Comparison between a balun with 50 Ω terminations at all ports and a balun with 50 Ω termination at unbalanced port and 25 Ω terminations at balanced ports. Second, 50 Ω baluns do not efficiently combine the capacitive device impedance and the inductive transformer impedance. Most active transistors do not have resistive input and output impedances. In fact, most power transistors have large input and output capacitances. Many transformers, on the other hand, are inherently inductive due the transmission lines and inductances. The extra inductance of the transformer often tunes the capacitive device impedance, which makes simpler matching circuit with lower loss and better bandwidth, as shown in Figure 3.3. 25 Figure 3.3. Impedance matching using the gate capacitance of the transistor and the leakage inductance of the balun. Third, the input and output baluns should be optimized separately for their own purposes. In power amplifiers, while the input and the output baluns share many similarities, some of the goals are different, so the design approach is also very different. For the input balun, the goal is to match the low impedance at the gate to the 50 Ω source. The approach is similar to the standard S-parameter input matching technique. Once the small-signal matching network is finished, a large-signal matching optimization can be done if the large signal model of the device is provided. The output balun design is slightly different. The goal is to present the desired load impedances at the fundamental frequency as well as the harmonics. For example, for a Class-E/Fodd,2 tuning, the switches of transistors should be presented with a load impedance of RL at the fundamental frequency, a short circuit at odd harmonics, and an open circuit at the 2nd harmonic. This is shown in Figure 3.4. It is clear that a balun may not satisfy the requirement of both the input and the output baluns because of different purposes for these baluns. 4. two types of low-frequency transformers are introduced. the traditional microwave baluns. This document presents a low-loss.26 Output Balun RL at fundamental Short at odd harmonics Open at 2nd harmonic RF output Figure 3. . impedance matching at the input and the output of the amplifier is very important. Also.2 Examples of Transformers and Baluns 3. and UHF Transformers In this section. but we were concerned that it would be difficult to make one at this frequency that would handle the large output power. which can be made much smaller than the conventional RF chokes. compact microstrip balun that performs impedance-transformation as well as balanced-tounbalanced signal conversion. at L-band. There are many different varieties of microwave baluns. However. VHF. the RF chokes are typically large in size.1 HF. at 1–2 GHz. are not practical due to their large sizes. Most of the published baluns are 50 Ω baluns. Since most high-frequency power devices have low input and output impedances.2. 3. Optimization goal for power amplifier’s output balun. Coil transformers are often used at lower frequencies. The balun in this design has a center-tapped choke. such as a hybrid ring. 2 Transmission-Line Transformers Transmission-line transformers are popular choices in VHF and UHF applications [35]. Finally.5. which would be too small at L-band. At L-band. It is therefore an ideal transformer for power amplifiers. Also.1. The Guanella 4:1 transformer balun is shown Figure 3. the length of the coils needs to be much less than a quarter wavelength. . The power handling capability is reduced.5. The impedance transformation of the transformer is N2. the configuration can be used as a center-tapped balun. which have very low input and output impedances. and the performance may be compromised.1.2. A coil transformer using a ferrite core (left).1 Coil Transformers The coil transformer is one form of the traditional transformers.27 3. This transformer can make high ratio of impedance transformation with relatively high bandwidth. 3. The second advantage of coil transformer is the complete isolation between DC and RF signals. For L-band applications. Figure 3. The equivalent circuit model of a center-tapped coil transformer balun (right). The key advantage of the transmission-line transformer is broadband impedance transformation. the ferrite cores used in the low-frequency transformers are too lossy at microwave frequencies. as shown in Figure 3.2. the manufacturing of these transformers are difficult.6. Figure 3.2. The detailed analysis of the balun can be found in [37]. there are also many different types of baluns [37].28 Port 1 Port 2 Port 3 Figure 3. An alternative to Guanella transformer balun is the Ruthroff transformer balun. there is no symmetry point in the Ruthroff transformer to be used as a center-tapped DC feed. and the device can be used as a balun. 3.8.7. Simplified schematic of a 4:1 Guanella balun. 3λ 4 λ 4 λ 4 λ 4 50Ω Figure 3. so additional DC-coupling capacitors need to be used. Compared to the coil transformer and Guanella transformer. The advantage of the balun is that it can achieve balanced outputs with a relatively easy implementation for an octave bandwidth. with the fourth port terminated with a 50 Ω load. . Three of the baluns are briefly introduced.7 shows a typical hybrid-ring coupler. Large RF chokes are also required for this balun transformer. A quarter-wavelength coaxial balun is shown in Figure 3. Schematic of hybrid-ring balun. The coupler is a four-port device. Also the DC and the RF signals are not separated.2 Microwave Baluns and Transformers At microwave frequencies. This balun can also achieve an octave bandwidth.6. While all microwave baluns shown can be implemented in L-band discrete power amplifiers. the size of the baluns is too large for this frequency band. The transformer is capable of combining up to four push-pull pairs of transistors (eight transistors) in a single circular configuration. the design of a compact power amplifier at this frequency will require more compact baluns.8. Since all these configurations require quarter-wave length transmission lines. λ 4 λ 4 Figure 3. it is difficult to implement the same structure in an L-band discrete high-power amplifier. While DAT has been implemented successfully in L-band Si integrated power amplifiers and HF discrete power amplifiers. The challenges and potential opportunities are discussed in Chapter 6.9. . Quarter-wave coaxial transmission line balun. The balun is typically realized in microstrip or coaxial cable forms. Another classic microwave balun is a Marchand balun shown in Figure 3.2.3 Distributed Active Transformer (DAT) The Distributed Active Transformer (DAT) was invented by Ichiro Aoki at California Institute of Technology [4][5][34]. The bandwidth of these baluns can be as high as a decade.29 λ 4 Figure 3. Microstrip implementation of Marchand balun. 3.9. because the L-band radar requires very compact T/R modules. such as coaxial cables. This is not suitable for production in large quantity. The structure of this balun is represented by Figure 3. Furthermore. as in an L-band phase array. some of the structures. The size of each microstrip has to be much less than one quarter wavelength. A microstrip balun (Figure 3. making the input and output matching of Vdd + Vdd + - . and it has a flexible geometry. The low coupling coefficient decreases the impedance transformation ratio of the balun.3 Compact L-Band Baluns The baluns reviewed in the previous sections are too large and do not meet the design specification. It is planar. At L-band.30 Vdd + + + - - Output - Vdd Figure 3. the drawback of the balun is the low coupling coefficient between the primary and the secondary inductors. However.11. this balun is smaller than the conventional microwave baluns. are not planar and require manual soldiering. 3. Schematic of the output circuit of a power amplifier with a Distributed Active Transformer.10.12) is designed using two small sections of magnetically coupled metals as the balun [38]. .31 the power amplifier difficult. The capacitive coupling between the inductors is represented by the capacitors between the inductors. A compact side-coupled microstrip balun on a dielectric substrate. The short microstrip lines are modeled as inductors L1 and L2. 3 1 2 Figure 3. which does not optimize the impedance transformation in power amplifiers.12 is also a 50 Ω balun. And the capacitive coupling between the microstrip lines and the ground plane is represented by capacitors to ground. A compact magnetic-coupled 50 Ω balun built on FR4 board.3. The balun shown in Figure 3.1 Lumped-Element Model The magnetically coupled microstrip lines can be modeled by the equivalent circuit model in Figure 3.13. The magnetic coupling is represented by the coupling coefficient k. 3. Figure 3.12.11. 32 Port 1 C1 k Port 2 C2 Port 4 Port 3 Figure 3.13. A four-port equivalent circuit model for coupled microstrip lines. 3.3.2 Tight-Coupling Microstrip Lines It is common in microwave circuits to achieve tight coupling between two coupled microstrip lines. The tight coupling often increases the bandwidth in microwave filters, couplers, and transformers. It is important to note that high coupling coefficient can be easily achieved in microwave and RF integrated circuits, due to the smaller size and spacing. Similar kinds of high coupling coefficients can also be achieved in low-frequency circuits using magnetic materials and coaxial lines. For discrete L-band high-power applications, coupling coefficients over 0.9 are extremely difficult to achieve even using the best PCB technologies. More often, parallel microstrip lines as shown in Figure 3.12 have a coupling coefficient of 0.35, which is not nearly enough for matching and impedance transformation. Two types of topologies are introduced next to improve the coupling between the coupling lines: interdigitated lines and broadside-coupling lines. In interdigitated configuration, the primary and secondary strip inductors are split into two or more strips. Primary and secondary strips are placed alternately, and the equivalent terminals are connected using small metal strips or bond wires shown in Figure 3.14. Using this method, the magnetic field is more confined inside the structure, which increases the magnetic coupling between the primary and the secondary inductors. 33 An alternative to the balun is using two strip inductors stacked up together as shown in Figure 3.15. The metal strips are separated by a thin dielectric layer. With the current multilayer printed circuit board (PCB) technology, the thickness of the dielectric layer may be as low as 125 μm. 3 3 1 2 1 2 Figure 3.14. Interdigitated balun with coupled inductors connected by wire bonds. 3 1 2 Figure 3.15. Broadside coupling balun with coupled inductors in a multilayered board. The baluns are simulated as 4-port terminals, and fitted in the model shown in Figure 3.13. Figure 3.16 and Figure 3.17 show the simulated coupling coefficients for side-coupled and broadside-coupled microstrip baluns. Simulated side-coupled and broadside-coupled microstrip baluns have coupling coefficients over 0.55 and 0.85, respectively. In practice, the coupling coefficient may be somewhat lower due to the constraint of circuit layout. 34 Coupling Coefficient 0.6 0.4 0.2 W=250um 0 0 200 400 Spacing, μm 600 800 W=750um W=1250um Figure 3.16. Simulated coupling coefficient of ideal interdigitated inductors. 1 Coupling Coefficient 0.8 0.6 0.4 0.2 0 0 W=250um 200 W=750um 400 W=1250um 600 800 Dielectric thickness, μm Figure 3.17. Simulated coupling coefficient of ideal broadside-coupling inductors. 3.3.3 Balance Optimization Since one end of the inductor shown in Figure 3.13 is grounded (in this case, let port 4 be grounded), the equivalent circuit is modified as Figure 3.18. Ideally, port 2 and port 3 should be balanced. However, from the circuit in Figure 3.18, unbalance clearly exists theoretically, because one of coupling capacitors C1 is connected between port 2 and port 1, the other coupling capacitor C2 is now connected between port 3 and ground. 35 Figure 3. Effectively. 2. this method is not helpful.18.18 would be perfectly balanced if capacitors C1 and C2 do not exist. So unless there is too much magnetic coupling involved. the problem with this approach is that increasing spacing also reduces the magnetic coupling between the microstrip lines. However. Lower the capacitive coupling between the two microstrip lines by increasing the dielectric thickness between the microstrip lines. Based on the simple assumption of a parallel-plate capacitance (3. In most cases. By reducing the width of the microstrip. a high magnetic coupling is desired for impedance transformation and bandwidth. we need to minimize the effects of those two capacitances. this approach decreases the area.1) 1. Use narrower microstrip lines to reduce the capacitance. and then reduces in capacitance and the unbalanced effect. where there may be a lot of capacitive coupling due to the large area of the microstrip baluns. which may or may not be a desired effect in the circuit design. Coupled inductors with one port grounded showing asymmetry. To minimize the unbalanced effect. C = ε rε 0 A d (3. The reduction in the capacitance between the microstrip lines reduces the unbalanced effect as well. the self inductance of the microstrip line increases. Port 2 and Port 3 shown in Figure 3.1). This method works well for broadside-coupled baluns. . we can optimize one or more of the variables in the equation. rather than high impedance levels. Use a lower dielectric constant. Most of the published baluns are 50Ω baluns. which do not perform impedance transformation. the most effect approach may be to reduce the load resistance of the balun. 3. If a 50Ω balun is used. the balanced-tounbalanced conversion can take place at low impedance levels.36 3.3.25 dB and the phase unbalance is no more than 5o. For a load resistance less than 10Ω. impedance matching is critical. Since the load resistance of the balun is in parallel with the capacitance. which in turn reduces the unbalanced effect. If the load resistance is much smaller than the reactance. Using lower dielectric constant can reduce the coupling capacitance significantly. Since RF power devices typically have low input and output impedances. This is another effective approach. In power amplifier applications. It is clear that the amplitude and the phase are well balanced for lower dielectric constant and lower load resistance.19. Figure 3. better balance can be achieved. the amplitude balance is less than 0.19 shows the amplitude and the phase balance as functions of load resistance and dielectric constant. Typical dielectric constant of a Duroid material ranges from 2 to 10. lowering the load resistance effectively shorts out the capacitance of the balun. It is recommended to calculate the reactance of the capacitances C1 and C2. Amplitude and phase differences for different load resistances and dielectric constants. 2 250 240 230 220 -6 210 -8 -10 -12 -14 1 1E1 1E2 200 190 180 1E3 A m plit ude D iff eren c e (dB ) 0 -2 -4 Figure 3.4 Input Impedance Transformation Since the input and the output of the RF power devices typically have low impedances. There is another advantage of this method. a matching circuit is required Pha se D iff eren ce (de gree) . . as in the case of sidecoupling lines. we are going to ignore the effect the capacitance to ground and the capacitive coupling between the inductors. The circuit is effectively a 2nd-order band-pass filter with LC matching. For example. The bandwidth is optimized individually for the balun and the input matching network.2) There are many different equivalent circuit models of Fig. In the ideal transformer shown in blue. as in the case of interdigitated balun.13. Therefore.20. The design of the impedance-transforming balun is based on the simplified equivalent circuit model of the balun shown in Figure 3. the impedance is reduced by a factor of 4. The mutual inductance of L1 and L2 is given by M = k L1 L2 (3. such as T-model and Pimodel. 4a. We propose an impedance-transforming balun.4) C' = C2 ⋅ N 2 (3. Here the analysis is based on a model with an ideal transformer shown in Fig 5(a) and (b).3) N= M L1 (3. the impedance is reduced by a factor of 10. it is difficult to achieve an input matching network that is optimized for the overall input circuit. 1− k2 L1 L' = k2 (3.5) The input matching circuit can be simplified to the schematic in Figure 3.1. which can be used for impedance matching as well as balanced-to-unbalanced conversion.37 for each gate of the devices as shown in Figure 3. the impedance multiplied by k2. if the coupling coefficient is 0.5. For this simplified approach. It is also clear from this equivalent circuit that the coupling coefficient k plays a very important role in the impedance transformation. If the coupling coefficient is 0.35. while performing well in magnitude and the phase balance.20. is introduced in parallel with the load resistance.3.38 This circuit can be used to optimize the input matching performance.0 185 184 phase_diff2 183 182 181 180 179 freq.5 Output Impedance Transformation The output impedance transformation is critical for the output power as well as the efficiency. Input matching optimization for the input balun.5 2.5 1. GHz Figure 3.5 Ω to 50 Ω using this topology. Simulated results for a 7. Figure 3. A key component.5 3. Figure 3.5 Ω to 50 Ω balun with a 3rd-order band-pass filter. The transistor is assumed to be a switch in parallel with an output capacitance. C2. . However. The output balun is substituted by two coupled inductors.22. and in series with a package inductance. The left vertical axis is for the input return loss and the output magnitude in dB. The detailed analysis is described in [39]. A simplified output circuit is shown in Figure 3.21.0 0. 0 -5 -10 -15 -20 -25 -30 0. 3.0 2.21 shows an example of a 3rd-order matching circuit from 7. simulation tools can also be used to optimize the values of the inductances and the capacitances.0 1. The right vertical axis is for the phase difference at the balanced ports. The simulation shows nearly octave bandwidth impedance transformation. the switch should see a high-impedance resonance at the fundamental frequency of operation. From Figure 3. for a transistor with a high output capacitance. Here in the figure. we see that we need to optimize the impedance looking away from the switch. can be also arbitrarily high.39 Figure 3. the susceptance increases with high output capacitance as well as high frequency of operation. in the ideal case. For the push-pull amplifier. The advantage is that the capacitance C2 is an arbitrary capacitor. Using this capacitance. not related to the output capacitance of the transistor. the output circuit becomes not as dependent on the transistor output capacitance as before. The second resonance (on the right) becomes significant as the frequency increases. the resonance on the left has been used for the fundamental frequency. the resonance frequency of the resonant circuit on the left is far below the desired operating frequency. as the operating frequency increases. As a result. Note that good bandwidth and desired operating frequency can be achieve only when tight coupling is achieved between the primary and the secondary inductors of the output balun. The resonance frequency. the switch actually sees two highimpedance resonances.4. Traditionally.22.23. A simplified output transistor and balun model for the output balun analysis. we can use the half-circuit analysis shown in Figure 3. For Class-E/Fodd topology. However. The package inductance also plays a significant role. indicated in the figure. . . One example would be a 900 MHz/1900 MHz GSM power amplifier.3. In both of these options. only a relatively short microstrip line and bypass capacitors are sufficient to separate DC and RF signals.24.6 Center-Tapped DC Feed and 2nd Harmonic Trap An RF choke is important to separate the DC bias from the RF signal in the amplifier. Also.23 are close to each other. In the low-frequency power amplifiers. the RF choke is very large in size. Typically in frequencies below microwave frequency. 3. it is common to feed the DC power for a push-pull amplifier at a symmetry point of the amplifier as shown in Figure 3. Sometimes.40 Figure 3. In higher frequency. if the two resonance circuits in Figure 3. we can tune both resonance impedances at two different bands to realize a dual-band amplifier. Potential applications with this topology are: broadband amplifiers and dual-band amplifiers. a large inductor is used for the RF choke. Furthermore. it is possible to combine the two resonances to design a broadband amplifier. A half circuit of the transistor and the balun. and there is no need for a very high-impedance inductor for RF choke. a quarter-wavelength microstrip is used for RF choke. For example.23. the harmonics of the amplifier are not likely to get into the DC power supply for a center-tapped DC feed. The center-tapped DC feed takes the advantage of the push-pull symmetry and the virtual ground. Schematic of center-tapped DC bias line. this topology has a natural symmetry point at the center of the primary inductor. A bypass capacitor provides an RF ground. It is a T-network with two inductors and a capacitor. it is desired to improve the current waveform using a second harmonic trap. k 2nd Harmonic Trap Figure 3. . One way to design such second harmonic tank is to use the network shown in Figure 3. The topology is then called a Class-E/Fodd.24. which is suitable for the DC feed. while many different balun topologies do not allow a centertapped DC bias line.25.25. for Class-E/F amplifiers with high output capacitances. At microwave frequencies. As discussed in Chapter 2.2 amplifier. Schematic of 2nd harmonic trap on the DC bias line.41 k DC Bias Figure 3. One convenient way to implement the second harmonic trap is on the center-feed bias line. S freq (2. .27.26. The simulated efficiency is improved by 5%. we see a comparison of the simulated output spectrum before and after the implementation of the second harmonic trap. From the Smith chart.5 GHz) sees an open circuit. Simulation of the 2nd harmonic trap in the Smith chart showing an open circuit for the 2nd harmonic.000GHz) Figure 3. In Figure 3. the second harmonic (at 2.000GHz to 3.42 The impedance at the second harmonic from the switch is shown in Figure 3. The second harmonic in the second graph is suppressed by 20 dB due to the second harmonic trap.26. The desired voltage waveform is nearly sinusoidal.28. This reduces the rms current as discussed in Chapter 2. The switch voltage and the switch current waveforms are shown in Figure 3. . The simulated efficiency improves by 5%. GHz Figure 3. and the desired current waveform has a waveform similar to a square waveform. GHz 60 40 Pout_spec 20 0 -20 0 1 2 3 4 5 6 freq. The output balun presents a load resistance at the fundamental frequency and high impedance at the second harmonic. Simulated output spectrum without (top) and with (bottom) the second harmonic tank.27.43 60 40 Pout_spec 20 0 -20 0 1 2 3 4 5 6 freq. 0 1.5 Time (ns) 1.0 0. The via structure and the air bridges in SONNET are sufficient to model these structures. In highefficiency power amplifier design. In narrowband applications. Switch current is near zero when the switch voltage is high. an EM simulator mostly for planar structures. a narrowband balun typically serves as a natural low-pass filter.5 2 0 Switch Current (A) 6 4 Id 8 Figure 3. This way.4 Balun Selection In this chapter. a full 3-D electromagnetic simulation is not necessary. Here are several factors that need to be considered when searching for a proper balun. The only true 3-D structures in the circuits are the vias and air bridges for the interdigitated baluns. 3. Low RMS current and low peak voltage. The question presented to power amplifier designers then is how to choose the balun that fits the need of a particular application.28.1 Bandwidth Someone may say that it is better to have a balun with the broadest bandwidth. Switch voltage is near zero when the switch current is high.44 Vd 60 50 Switch Voltage (V) 40 30 20 10 0 0. 3. For the most part of the design. this is not always the case. which gives low harmonic levels. . is used for all electromagnetic simulation. and a new balun was introduced. In a push-pull power amplifier. which is beneficial. it is often a good idea to have a balun which has good balance up to twice the fundamental operating frequency. The switching voltage and current waveforms.4. SONNET. many different baluns were reviewed. in applications lower than GHz level. we typically would like to have compact baluns to reduce the overall size of the amplifier. transmission-line transformers. most baluns belong to one of the following two cases: (1) the size of the balun is much less than a quarter wavelength. The amplifier and phase balances are compromised as the assumption is violated. and thereby can be assumed as coupled inductors. the third harmonic can be tuned by a harmonic trap.4. baluns typically use inductive coupling as a means of transformation. From this perspective. and higher harmonics are filtered by the balun. It is then quite clear that selecting a compact balun structure depends on the operating frequency and the process technology. In the first case. Of course. For example. and the new baluns introduced in this chapter. but only in very limited bandwidth. and harmonic tuning is very difficult. which can be used this type of applications. Conventional microwave baluns. In these baluns. In this case. Most conventional microwave baluns have relatively narrow bandwidth up to an octave. These baluns typically have good performance as long as they are close to a quarter wavelength.or even decadebandwidth. such as Marchand baluns and hybrid rings. the lengths of the transmission lines are much less than a quarter wavelength (typically less than one-sixth of a quarter wavelength). Such baluns include coil-transformers. Good balance may be achieved sometimes. have approximately the size of a quarter wavelength. . as well as the coupling structure used in Discrete Active Transformer.2 Size As amplifier designers. wideband baluns must be used. Coil transformers and transmission-line transformers are some of the broadest bandwidth baluns. there are many applications. 3. In applications above 30 GHz.45 the second harmonic of the amplifier is suppressed due to the symmetry of the amplifier. which require multioctave. and (2) the size is comparable to quarter wavelength. it is very difficult to implement a compact balun using conventional microwave balun structures. inductive-coupling balun structures are difficult due to the process technologies. the characteristic impedance of the coaxial cable should be between 10 Ω and 50 Ω. realizable in a particularly processing technology. Basically. between a few Ohms. these transformers are scaled down in size and up in frequency. it is relatively easy to make a transmission line with characteristic impedance between 10 Ω and 50 Ω. 3. many HF. if coupled inductors are used in the balun. . For example. if a coaxial cable is used as a part of the balun.4. the reactance of the inductor should be between 10 Ω and 50 Ω.46 It should be noted that with advanced processing technologies.3 Impedance Level and Impedance Transformation For power amplifier applications. For most processing technologies. It is important to consider impedance level of the components. the impedance level is typically low. For the same transistor technology. and the impedance of the transistor is 10 Ω. VHF and UHF baluns are rediscovered to be useful at frequencies up to a few gigahertz. and efficiency requirements make this amplifier difficult to design. As different improvements are implemented in the different generations. Two types of baluns are implemented in the power amplifiers: interdigitated baluns and broadside-coupling baluns. The specifications of the L-Band high-efficiency power amplifier are listed in Table 4. Table 4.5 W 3V 23 pF 30 W . there are not many choices for proper devices. the implementation of four generations of power amplifiers and the measurement results are presented.47 Chapter 4 Implementation of Power Amplifiers In this chapter.2.1 Amplifier Specifications Parameter Operating frequency Output power Efficiency Gain Value 1220 –1300 MHz 30 W 70% 10 dB Since most of the transistors in L-band are pre-matched for wireless base station applications at 1. At the end of the chapter.2 Specifications of Freescale MRF 284 Maximum Drain-Source Voltage Maximum Gate-Source Voltage Total Device Dissipation Gate Threshold Voltage Output Capacitance (Vds=26 V f=1 MHz) Output Power 65 V ±20 V 87. Table 4. There is also a comparison between the measurement results with the best published results. Some key specifications are listed in Table 4. The combination of output power.9 GHz. the results of different versions of amplifiers are compared. Freescale MRF284 LDMOS devices are chosen as the active devices of the amplifier. bandwidth.8-1. the measurement results improve as well.1. These devices are unmatched. SONNET. 800 MHz Class-E/F power amplifier with interdigitated baluns.4. The output power and drain efficiency are measured and shown in Figure 4. Input Balun Output Balun Figure 4.1 800 MHz Power Amplifier Using Interdigitated Baluns Figure 4.3.2. Interdigitated baluns are used. Amplifier Research model is used as the driver amplifier.1. The model is verified using the electromagnetic simulator. so the fingers are connected using wire bonds. The 5 mil spacing is the smallest that can be fabricated. The baluns are gold plated.1 shows a picture of the first design of the Class-E/F power amplifier. The measurement block diagram is shown in Figure 4.1.1 Implementation and Measurement 4. The width of the fingers is 20 mils while the spacing between the fingers is 5 mils. The power measurement was performed using a Bird power meter. The amplifier is built on FR4 board with a dielectric constant of 4. The measurement was performed . and a photo of the measurement setup is shown in Figure 4. and the close spacing is used to maximize the coupling between the fingers.48 4.3. Two LDMOS transistors are placed side-by-side as close as possible. The balun structure is modeled using the equivalent circuit model discussed in Chapter 3. The primary inductance has four fingers. while the secondary inductance has three fingers. This way the inductance between the drains of the amplifiers can be reduced. . At 30 W output power level.2. Figure 4. DC Power Supply Signal Generator Driver Amplifier Directional Coupler Attenuator DUT Directional Coupler Power Meter (Output Power) Power Meter (Reverse Power) Power Meter (Forward Power) DC Power Supply Spectrum Analyzer Figure 4. Block diagram of the measurement setup.49 at 800 MHz. 12 dB gain and 64% drain efficiency are achieved.3. A typical measurement setup for the power amplifier. There are a few other issues with the design. the lengths of the fingers of the baluns are limited by the size of the transistors. in this configuration.1. This introduces unbalance due to the capacitance between the fingers and the capacitance to ground. The amplifier is fabricated on FR4 material. another configuration of the amplifier is designed to have the drains of the transistor facing each other. Gain and PAE vs. 4. The picture of the amplifier is shown in Figure 4. The unbalance causes reduction in output power. The operating frequency is less than the target 1220–1300 GHz.2 900 MHz PA Using Interdigitated Baluns In this version of design. In order to reduce the length of the balun. The .50 20 80 70 15 Gain (dB) 60 50 10 40 D r a i n E f f ic i e n c y ( % ) 5 30 W Gain =12 dB Efficiency = 64% 0 10 20 Output (W) 30 40 30 20 10 0 0 Figure 4.5. gain and efficiency. several significant changes are made to the amplifier. This configuration is discussed in the next section. because the operating frequency is inversely proportional to the square root of the capacitance. One way to increase the operating frequency is to reduce the self-inductance of the output balun. The input matching circuit is also not optimized. output power for 800 MHz PA.4. The lengths of the baluns are not much smaller than a quarter-wave length. Some of these issues are addressed in the second version of the amplifier. However. The reason is the high output capacitance of the transistors. which is in series with the output balun. increases the operating frequency of the amplifier. the amplifier suffers from a low-frequency oscillation. more input matching circuits are included. which is critical for the power. Using this layout. in theory.51 width of the balun fingers are 25 mils. Another significant change is to have a much shorter input balun compared to the previous version. and improves the balance of the balun. The output power. 900 MHz Class-E/F power amplifier with interdigitated baluns. The amplifier had a similar performance to the previous version. The first change of the amplifier is to have the drains of the transistors facing each other. gain and efficiency are similar. It is partially effective. .5. A ferrite bead is used on the gate bias line to reduce to the oscillation. In addition to the input balun. The reduced length of the output balun did not improve the operating frequency as expected because of the significant package inductance of the transistors. This change. In this case. RF Input Output Balun Input Balun Drain Bias Gate Bias RF Output Figure 4. and the spacing between the fingers is 5 mils. Copper wire bonds are used to connect the interdigitated fingers of the baluns. However. which is not identified using theoretical models. the lengths of the baluns are reduced significantly from the previous design. This also helps improve the balance of the push-pull amplifier. the operating frequency increases slightly to 900 MHz. gain and efficiency. The output balun connects between the leads of the drains of the transistors. The layout and the photo of the amplifier are shown in Figure 4. The multilayer configuration is enabled by the multilayer PCB technology. This minimum thickness limits the coupling coefficient between the layers. As in the previous version.52 Another key problem with this design. The vias between the first and the second metal layer are made. 5 mil 62 mil Figure 4.6.3 1200 MHz PA Using Broadside-Coupling Baluns on FR4 Broadside-coupling baluns are used in this version of power amplifier. The size of the amplifier is 3 cm by 3 cm. The amplifier is built on a three-layer PCB using FR4 material shown in Figure 4. which has a dielectric constant of 4.6. Cross-sectional view of the multilayer PCB built on FR4. which is 5 mils. In order to improve the coupling. The dielectric layer between the first and the second metal layer is a 5 mil core of FR4 material. the drains of the transistors face each other.3. The vias are shown in red. is the poor coupling coefficient between the primary and the secondary of the input and output balun. narrow transmission line to increase the impedance at the secondary of the output balun. we use the minimum separation between two layers.8. .5. Since we want to minimize the separation of between the primary and the secondary inductors in order to improve the coupling coefficient. 4. while the gates are away from each other. directly below the primary inductor. we can see that the RF output has a long.7 and Figure 4. multilayered board is used to implement broadside-coupling baluns in the next version. as described in Chapter 3. Then the two boards on connected together for the final multilayered board. The second dielectric is a 62 mil core and its vias are built. From Figure 4. and the secondary inductor is on the second level of PCB.1. The primary inductor is on the top layer of PCB. The main reason is to improve the coupling coefficient between the primary and the secondary inductors. This simple output transformation structure is compact and low loss. This also reduces the self-inductance of the output balun. . the overall width of the balun is increased by a factor of 2.5.53 One advantage of this wide balun is that the impedance of the transmission line is low. The simulated loss of the output balun is 5%. Figure 4. Compared to the interdigitated version. a center-tapped DC bias line is used in the balun. The second advantage of the wide baluns is reduced loss. which is very suitable for impedance transformation at low impedance level. along with the output balun. Again. The power amplifier is simulated in Agilent ADS. only one output capacitor is used as the output matching element. Layout of 1200 MHz Class-E/F power amplifier with broadside-coupling baluns. For the output matching. using SONNET.7. The primary inductor in the second layer is directly below the secondary inductor. The input baluns have reduced size in order to improve the input magnitude and phase balance.9. Port 2 CenterTapped DC Bias Line Port 1 1 mm Via to Ground Port 3 Figure 4. On the input side. A centered-tapped DC feed is used for the input balun with a series ferrite bead as an RF choke.54 RF input 3 cm x 3 cm Output Balun Drain Bias Gate Bias RF output Input Balun Figure 4. wide lines are used for input matching due to the low-impedance level at the gate of the transistor. .8. 1200 MHz Class-E/F power amplifier with broadside-coupling baluns on FR4. The lossy nature of the ferrite bead is used to eliminate oscillation. Photo of the center-tapped input balun. 55 The performance of the amplifier is shown in Figure 4. 60 50 40 30 20 10 0 1040 0 5 10 15 1120 Output Power. Gain. Figure 4. output Power at 1075 MHz. The 3 dB bandwidth is 45 MHz. All measurements were performed with a continuous wave (CW) input signal.10.11. dB Figure 4.11. dB 10 5 0 0 20 40 60 Output Power. The output power spectrum of the amplifier shows excellent suppression of harmonics of the fundamental frequency. % Return Loss. Figure 4. The bandwidth is limited by the input matching.10 shows that at 1075 MHz. W 60 40 20 0 PAE. The power amplifier is simulated in Agilent ADS. The simulated loss of the output balun is 5%. MHz Figure 4. output power is 44 W while the gain is 12 dB and PAE is 60%.12 shows the output frequency spectrum of the amplifier. using SONNET. frequency. Figure 4. W 1060 1080 1100 Frequency. and the 3rd harmonic is also . The 2nd harmonic is 45 dB below the fundamental. Output power and return loss vs.10 and Figure 4.11 shows the frequency response of the power amplifier. Gain and efficiency vs. the separation between the first and the second metal layer is 7 mils. 5 mil 2 mil bonding film 62 mil Figure 4. The coupling coefficient between the layers is thereby less than the previous version. The push-pull configuration reduces the level of the even harmonics.12.13.6 [40]. Effectively. This board is chosen because it has lower dielectric loss than FR4 board. Dielectric between the second and the bottom metal layer is 62 mils. and it has a lower dielectric constant. The cross-sectional view of the multilayered board is shown in Figure 4. Dielectric between the top and the second metal layer is 5 mils of RF 5880 plus 2 mils of bonding film which is made of a low-loss dielectric with a dielectric constant of 2. the narrow-band nature of the output balun helps suppress both even and odd harmonics. The duroid material is softer than FR4 material. Cross-sectional view of the multilayer PCB built on FR4. Frequency spectrum of fundamental and harmonics 4. In addition. The dielectric constant is 2.56 45 dB below the fundamental. .4 1100 MHz PA Using Broadside-Coupled Baluns on Duroid The multi-layered boards are manufactured on Rogers RT/Duroid 5880.2.1. which improves the balance of the baluns. Figure 4.13. the building process is also more difficult. C C5 C C3 C C4 C C7 M BEND Bend1 C C6 TLIN TL3 C C1 TLIN TL1 MRF_ROOT_MODEL MRF1 TLIN TL2 M RF_ROOT_MODEL M RF2 C C2 TLIN TL4 C C8 M BEND Bend3 MLIN TL9 C C13 MBEND Bend2 C C9 MLIN TL5 MSTEP Step1 C C11 MLIN TL7 M LIN TL8 XFERTAP XFer1 C C12 MSTEP Step2 MLIN TL6 C C10 MLIN TL10 Input Balun C C14 M BEND Bend4 RF Input Port P1 MLIN TL11 C C15 Figure 4. Also shown on Figure 4.1 GHz.57 The matching circuit is significantly improved from the previous version in order to extend the bandwidth of the amplifier. Input matching network of the L-band power amplifier.14. The peak power-added efficiency is 65%.5 cm x 5 cm Output Balun Multi-Layered Microstrip Lines Drain Bias Port 2 Port 3 Gate Bias Input Balun CenterTapped DC Bias Port 1 Vias RF Input Figure 4. 1200 MHz Class-E/F power amplifier with broadside-coupling baluns on Duroid.16 for comparison are the gain and PAE predicted by an ADS harmonic-balance simulation.15.14. and the photo of the amplifier is shown in Figure 4. the peak output power is 60 W with a drain bias of 32 V.15. RF Output Size: 3.17 show the measured performance. The 3-dB . At 1. The circuit schematic is shown in Figure 4. This suggests that it may be possible to improve the gain. The measured PAE is quite close. Figure 4. but the measured gains are 2 dB to 3 dB low.16 and Figure 4. Figure 4. 16 14 12 Gain (dB) 10 8 6 4 2 0 0 10 20 30 40 50 60 70 Output Power (W ) 80 70 60 50 40 30 20 10 0 Efficiency (%) Figure 4. The current waveform has a relatively square shape. Gain and input return loss vs. The largest harmonic components are the 3rd and 5th.19 shows the measured output power spectrum. at −40 dBc. The voltage waveform is nearly a half sinusoid. This reduces the peak voltage compared with a Class-E amplifier. 12 10 -5 Gain (dB) 8 6 4 -15 2 0 950 1000 1050 1100 Frequency (MHz) -20 1150 -10 0 Input Return Loss (dB) Figure 4.18. The simulated waveforms from ADS are shown in Figure 4. Gain and PAE vs. output power. frequency. reducing the rms current compared to .16. and the solid lines are measured results. The dash lines are simulated results.17.58 bandwidth is 150 MHz. 5 Time (ns) 1. 0 Power Spectrum (dBc) -10 -20 -30 -40 -50 -60 0 2 4 6 8 10 Frequency (GHz) ≥40 dBc for all harmonics Figure 4.0 0. and half the loss in the capacitors. The eye diagram and the phase trellis are shown in Figure 4. . the MSK signal is generated to feed the power amplifier.2%. such as MSK. and the output is measured by the analyzer. Output power spectrum.59 a Class-E amplifier. The switching-amplifiers can be used for wireless communications applications which can tolerate strongly nonlinear effects of the amplifiers. Using the digital signal analyzer.5 0 4 Switch Current (A) 6 8 Figure 4.18. This helps to reduce the on-resistance loss in the amplifier. 60 50 Switch Voltage (V) 40 30 20 2 10 0 0. Constant envelope signals. can be faithfully reproduced. with half the loss in the metal. The simulated loss of the output balun is 5. The loss of the Duroid coupling layer was negligible.0 1.20. Simulated waveform of Class-E/F amplifier.19. frequency. gain and PAE vs.22. Output power.60 Figure 4. 4. .21 and Figure 4.20. The peak measured output power is 74 W with a peak PAE of 67%. and vias are properly modeled. The 1 dB bandwidth is 170 MHz.1. The improved measurement results are shown in Figure 4. 70 Pout (W) & PAE (%) 60 50 40 30 20 10 0 1100 1150 1200 Frequency (MHz) 1250 Pout PAE Gain 14 12 10 8 6 4 2 0 1300 Gain (dB) Figure 4.5 1200 MHz PA Using Broadside-Coupled Baluns on Duroid The previous amplifier is tuned with better capacitor models with series inductance. Measured eye-diagram and phase trellis using an MSK signal.21. Freq 1 2 3 4 5 800 MHz 900 MHz 1220 MHz 1100 MHz 1210 MHz Power Eff. 4.61 14 12 10 Gain (dB) 8 6 4 2 0 0 20 40 Output Power (W) 60 80 Gain PAE 70 60 50 40 30 20 10 0 PAE (%) Figure 4.2 Performance Comparison The following table summarizes the performance of the amplifiers during different iterations.22. Table 4. output power at 1220 MHz. Gain and PAE vs. 30 W 30 W 35 W 60 W 74 W BW Comment Poor coupling coefficient Package inductance is significant Stronger coupling coefficient Insufficient input matching Lower frequency due to passive component modeling Better performance than previous versions 56% N/A 52% N/A 63% 80 MHz (3 dB) 65% >150 MHz (3 dB) 67% 170 MHz (1 dB) The final table compares the performance of this power amplifier to comparable recently reported amplifiers.3 Performance Summary of Different Versions of Amplifiers Ver. Our amplifier has an output power five times larger than the other . The bandwidth of the amplifier is also significantly higher than the other amplifiers.0 GHz Ericsson Si LDMOS PTF 10135 6 cm x 20 cm Le Gallou et al.62 amplifiers.21 GHz Motorola Si LDMOS MRF 284 5 cm x 3. Table 4.4 Comparison of Performance with Published Results This Work Power Gain PAE BW Class Freq. with an area five times smaller. [41] 13 W 14 dB 58% N/A Class D-1 1.5 GHz UMS Custom GaAs HBT Confidential Adahl et al.0 GHz Motorola Si LDMOS MRF 282 10 cm x 10 cm Size . Device 74 W 11 dB 67% 150 MHz (1 dB) Class E/Fodd. [43] 10 W 13 dB 66% 50 MHz (1 dB) Class E 1.2 1.5 cm Long et al. [42] 10 W 13 dB 66% >50 MHz (3 dB) Class F-1 1. The theme of this chapter is to introduce the nonlinear bifurcation stability analysis of power amplifiers. the technique is applied to the L-band power amplifier discussed in previous chapters. When oscillations occur. eliminating one oscillation leads to the onset of another. spurious oscillations occur due to many reasons and are not easy to predict due to the complexity of the circuits. Oscillations may degrade the gain and the efficiency of the power amplifiers. . leading to oscillations at sub-harmonic or incommensurate frequencies. cause interference with other applications.63 Chapter 5 Bifurcation Stability Analysis of L-Band Power Amplifier Power amplifiers are likely to exhibit instabilities. Stabilization of power amplifiers can be one of the most frustrating parts of the design of power amplifiers. and predicts the behaviors of the oscillations. the process of determining the causes of oscillation may be lengthy. In particular. effective and accurate theoretical prediction of these oscillations is a critical part of power amplifier design. Since oscillations are common phenomena in power amplifiers. in many other situations. Based on the results of the stability analysis. This approach may take much iteration without eliminating the oscillations. When designing power amplifiers. Trial-and-error is a common approach to stabilize the amplifier. effective stabilization techniques can be designed to ensure globally stable amplifiers. and even destroy the active devices in the power amplifiers as well as other elements in the transmitters and receivers. this theoretical approach effectively detects the oscillation in the amplifier. Sometimes. Based on the information provided by the analysis. designers often follow a set of general guidelines based on previous experiences and intuition. However. three different stabilization circuits are introduced to effectively eliminate the oscillations in the amplifier. Taking into account of strong nonlinearity in power amplifiers. These guidelines are frequently helpful in reducing the probability of oscillations. .64 5. Since most high-efficiency amplifiers are driven deep into saturation and are highly nonlinear. These measures often eliminate low frequency oscillations due to bias networks and DC power supplies.1 Introduction to Stability Analysis There are many causes of instabilities in power amplifiers. These oscillations cannot be detected with conventional techniques based on the k factor. the linear techniques are limited only to the detection of the oscillations. Some of the causes of oscillations can be solved by simple experimental methods. In the case of push-pull amplifiers. Their detection requires a large-signal stability analysis of the steady-state solution. Furthermore. Addition of resistive elements such as ferrite beads can be helpful in providing damping effect on oscillations. and thermal feedback. the bias network needs careful placement of bypass capacitors and chokes inductors. This is particularly true for linear and weakly nonlinear power amplifiers operating in Class-A and Class-AB modes. sub-harmonic oscillations. parametric oscillations due to nonlinear capacitances. Push-pull amplifiers may have common-mode oscillations and differential-mode oscillations [46][47]. resonant tanks in bias networks. the oscillations often occur from a certain level of input power or nonlinear capacitances of the active devices. For example. Some of the common causes include linear gain and feedback. the linear techniques do not give information about the amplitude and the phase of the oscillation. interaction with DC power supplies. but do not describe the behaviors of the oscillation described previously. the k-factor may also be used to detect the potential oscillation. The most difficult situations deal with situations beyond small-signal or linear analysis. hysteresis and even chaotic behaviors [44][45]. In some nonlinear power amplifiers. The oscillations may exhibit different behaviors such as mixer-type oscillations. the onset of an oscillation does not require an RF drive. In such cases. Other oscillations may be detected by linear stability techniques based on the k factor. This technique takes into account the nonlinear elements in the power amplifiers.2) Output stability circle: S12 S 21 S 22 − Δ 2 2 rL = (5. and accurately predicts the conditions of the onset of oscillations. These circles provide a set of source and load impedance such that the magnitudes of the input and the output reflection coefficients are less than one. Input stability circle: S12 S 21 S11 − Δ 2 2 rS = (5.1.1 Stability Analysis Based on Linear S-Parameter The most common stability analysis in microwave amplifiers is performed based on twoport S-parameters. 5.65 In this section.1) – (5.4).1 Methods in Stability Analysis 5. The stability circles can be graphically represented on the Smith chart. and a new bifurcation analysis technique based on harmonic balance (HB) is introduced.1.1. With the two-port small-signal S-parameters at a particular frequency and a particular bias condition.4) . The detailed derivation of the method can be found in [48] and [49]. It also provides information describing the behavior of the oscillation.3) CL (S = 22 * − ΔS11 2 ) S 22 −Δ 2 (5.1) CS (S = 11 * − ΔS 22 2 ) 2 * S11 − Δ (5. the input and output stability circles can be derived. The radii and the centers of the stability circles are given in (5. which is valuable to devising stabilization techniques. the linear stability techniques are reviewed. the amplifier is potentially unstable. k >1 (5. This is particularly true for the variable capacitances in power amplifiers. Practically. the oscillation may occur due to the nonlinearity of the capacitors. First. they have many limitations when used in stability analysis of nonlinear power amplifiers. the input signal is small signal.66 where Δ = S11 S 22 − S12 S 21 (5. an array of stability circles can be drawn by sweeping the frequency and the bias conditions of the amplifier.8) and Δ = S11 S 22 − S12 S 21 (5. the condition is only valid at one frequency and bias condition. As the voltage at the gate and the drain of the transistors change.6) and Δ <1 (5. the capacitances of the transistors show strong nonlinearity. Again. the k-factor analysis is often used.7). the linear analysis technique does not account for the instability caused by the nonlinear elements in the transistor.6) – (5. For the unconditionally stable condition. When the result of the interaction shows negative resistance.9) While the k factor and the stability circles are helpful tools for stability analysis of linear amplifiers. As a result.5) The stability circles focus on the interaction of the source and load impedances with the input and output impedances of the amplifier. . The unconditionally stable criteria are given in (5.7) where k= 1 − S11 − S 22 + Δ 2 S12 S 21 2 2 2 (5. k-factor may still be a nice choice. While some power amplifiers exhibit selfbiasing oscillations. There is no prediction of the amplitude and the phase of the oscillation. many power amplifiers do not exhibit oscillation. We will discuss other analysis tools to obtain these pieces of information. some power amplifiers exhibit chaotic behavior. The analysis is available in many commercial microwave circuit simulation packages. 5. Thirdly.1. Instead. it only requires one set of S-parameter measurement data. They are therefore important to devise effective stabilization techniques. In the local linear stability analysis.67 Second. k-factor analysis does have several practical advantages. even if the k factor is below 1.2 Local Linear Stability Analysis The purpose of this section is to give a brief overview for the linear stability analysis technique. and it takes very little time on today’s computers. a linear circuit can be represented by the following differential equation with initial conditions. no oscillations are observed. The analysis does not require accurate nonlinear models of the active devices. Furthermore. the k-factor analysis does not provide information about the nature of the oscillation. unless they are driven by an external RF input source. but only one oscillating frequency is observed.1. which are often difficult to find. . The detailed mathematical derivations can be found in [44]. the linear analysis technique does not provide the onset condition of oscillation. If a quick and simple analysis is needed. In general. It is very simple to calculate. such as the drive frequency and the input power. the k factor may be below 1 for a range of frequencies. For some power amplifiers. As the final words in this section. The amplitude and the phase of the oscillation provide useful information about the nature of the oscillation. a set of linear ordinary differential equations (ODEs) are used to state variables such as voltages and currents in the circuits. For other power amplifiers. and the k factor does not predict it. The information is used to interpret the simulation results of the actual power amplifiers. The result of the analysis shows that the lumped circuit is stable if all non-zero eigenvalues ( λ ) of the matrix ( A = −G −1C ) have a negative real part. In the simplest case.13) have a negative real part. of the transfer function given by sj = 1 λj (5. real or complex. dx (t ) + Gx (t ) + u (t ) = 0 dt x (0 ) = x 0 C (5. C represents the generalized capacitance matrix. The solution in the frequency domain is then converted back to the time domain using inverse Laplace transform. it is possible to solve the differential equation in the frequency domain using Laplace transform.10) where x are the state variables such as node voltages and branch currents. stability conditions can be discussed using the solutions of the following differential equation. Re{λ j } < 0 (5. u (t ) represents the vector of independent sources. Re{s j } < 0 (5.12) This result is equivalent to all poles ( s ). While solving the differential equations in the time domain is difficult. G represents the generalized conductance matrix. t ) dt x (0 ) = x0 (5.11) where x (t ) represents the vector of node voltages.68 dx = f (x . in which a circuit contains only passive lumped elements.14) . the stability analysis cannot be restricted to the linear case.1. and get the perturbation equation (5. By carefully examining the state variable X (s ) .3 Nonlinear Stability Analysis Nonlinear bifurcation analysis extends the techniques described in the previous section to nonlinear regime.16). it can be represented by the ratio of two functions of s. if X (s ) have no poles with a positive real part.15) where y (t ) is a matrix made up of the time-domain impulse responses of the linear distributed elements. C t dx (t ) + Gx (t ) + ∫ y (t − τ )x (τ )dτ + u (t ) = 0 −∞ dt (5. We take the Laplace transform of (5. For zero-input case ( u (t ) = 0 ).1. In the next section. . 5. Introduce a small perturbation δx (t ) Take the linearization of the differential equation. The stability conditions of a microwave distributed circuit can be represented conveniently using the Nyquist plot. we will expand the theory to accommodate the nonlinearities in the power amplifiers. We use a modified equation from the previous lumped element analysis. the circuit is stable.69 The stability analysis of microwave distributed circuit requires frequency-domain analysis and the use of Nyquist criterion. The general microwave nonlinear circuit is represented by t dq ( x (t )) + f ( x (t )) + ∫ y (t − τ )x (τ )dτ + u (t ) = 0 −∞ dt (5.16) Obtain the solution of the nonlinear differential equation (5. Since power amplifiers are nonlinear circuits.17).15) and solve for the state variables in the frequency domain. drive frequency.70 t d [C(x (t )δx (t ))] + G (x (t ))δx (t ) + ∫−∞ y (t − τ )δx (τ )dτ = 0 dt (5. two conditions are considered.18) Condition for local stability: a nonlinear circuit is locally stable around the steady-state solution x0 (t ) if the solution δx (t ) of the perturbed system goes to zero as t goes to infinity. and resistors). The bifurcation points are defined as the boundary points between two different types of behaviors in the power amplifier.17) where ⎡ ∂f ⎤ ⎡ ∂q ⎤ C( x (t )) = ⎢ ⎥ and G ( x (t )) = ⎢ ⎥ ⎣ ∂x ⎦ x = x0 (t ) ⎣ ∂x ⎦ x = x0 (t ) (5. Qualitative changes of behavior may include the onset of an oscillation from an amplifier operation. One special case of the second condition is considered. but difficult to implement in practical situations. and circuit elements (capacitors. Generally. or the DC solution of the circuit. The second condition corresponds to the time-varying operating condition of the circuit. and the onset of a chaotic spectrum from an oscillation. Often these mathematical approaches are relatively easy to understand as a concept. The bifurcation analysis studies the qualitative change in the behavior of a system as a function of system variables. the onset of a second oscillation from the first oscillation. In the case of power amplifiers.2 Nonlinear Bifurcation Analysis Many nonlinear analysis techniques require complex mathematical derivations. The key advantage of the methods described here is that they can be quickly implemented in a commercial circuit simulator. the bifurcation analysis is used to analyze the dramatic changes of behavior of the amplifier due to changing variables. . such as the input power. bias voltages. 5. The first condition corresponds to an equilibrium point of the circuit. It is when the operating condition is a periodic in time. inductors. The vectors of the state variables. .. mk = −∞ ∞ ∑X ∑Y ∞ ∞ m1 ... the state variables. Let us consider the general nonlinear circuit used in HB with three kinds of elements: state variables x n with 1 ≤ n ≤ Q . g S (t )) In HB analysis.2. nonlinear elements y m with 1 ≤ m ≤ P .. f k are considered in the HB simulation. and the independent generator can be represented by Fourier series x (t ) = y (t ) = g (t ) = m1 = −∞ ∑ ∞ ∞ ...20) m1 = −∞ ∑ mk = −∞ ∑G m1 .......71 Since the oscillations start at the bifurcation points. nonlinear components..19) g (t ) = ( g1 (t ).+ mk ωk )t m1 = −∞ ∑ ∞ mk = −∞ m1 .. the set of frequencies must be chosen beforehand. xQ (t )) T T T y (t ) = ( y1 (t ). In other words...+ mk ωk )t (5... all potential oscillation frequencies in the power amplifier must be chosen prior to HB simulation... mk e j (m1ω1 +.... the nonlinear elements and the independent generators are represented by x (t ) = (x1 (t ).1 Oscillation Detection Using Small-Signal Generator The nonlinear bifurcation analysis considered in this chapter is based on Harmonic Balance (HB) simulations [50]. HB will not be able to analyze it.. y 2 (t ). mk . g 2 (t ). x 2 (t )... and independent generators g l with 1 ≤ l ≤ S . . because only the linear combinations of frequencies f1 .... Once the frequency basis of k frequencies is chosen. and effectively eliminate these bifurcation points. Harmonic Balance is widely implemented in commercial circuit simulators to simulate the large-signal or the nonlinear behavior of the power amplifiers..+ mk ωk )t e j (m1ω1 +.mk e j (m1ω1 +. It is important to realize that choosing the initial frequency basis is critical to HB simulation. If any of the oscillation frequencies is missing. 5. the goal of this work is to detect the complete set of these bifurcation points (or bifurcation boundary)..... y P (t )) (5. 1.21) and (5. In order to pick a complete set of frequencies for the HB. Common choices for such nodes are the gate and the drain of the transistors. After defining the current source i s . Depending on the complexity of the circuit. the current source needs to be inserted at all critical points of the amplifier. In complicated circuits. Under the large-signal operation determined by HB.1. we see that only discrete frequency values are represented in the Fourier series representation.22). a small-signal current source is inserted at one node of the amplifier shown in Figure 5. such as distributed active transformer (DAT) or multi-stage power amplifiers. This approach is referred as the conversion matrix or large-signal/small-signal approach [50]. and the small-signal response of the system is calculated. the system is linearized. Figure 5.72 Again. the smallsignal current source may be inserted at different nodes of the circuit to detect the complete set of oscillation frequencies. we can also determine the voltage at the node of the amplifier v s . The small-signal source cannot disturb the large-signal operation of the power amplifier. We can then define an impedance function and an admittance function shown in (5. Conversion matrix approach to detect oscillations using a small-signal current source inserted at one node of the power amplifier. . There may be unstable zeros with positive real parts appearing in the right-hand side of the complex plane. However. Since operation of power amplifier needs to be analyzed using nonlinear simulation and the current source is a small-signal source. The values of the poles and zeros are listed in Table 5.2. three different methods are introduced here to detect potential oscillation.21) Y= (5.1 and Table 5. where f in is the drive frequency of the amplifier. an L-band power amplifier is stable under a particular set of operating conditions.2 and Figure 5. The poles with positive real parts are on the right-hand side of the complex planes.2. There are two sets of unstable poles. and no oscillation is observed. All frequencies f a for 0 < f a < f in need to be examined carefully.3 illustrate two of the possible cases in power amplifiers. In some cases. Once the impedance function Z and the admittance function Y is calculated.2. In those cases. the pole-zero cancellation occurs. both sets of unstable poles are canceled by the two sets of unstable zeros of the admittance function. . respectively. Z and Y can be calculated easily while sweeping the frequency of the small-signal current generator.22) Using commercial simulation tools such as ADS.1 Pole-Zero Identification Technique The poles and the zeros of the impedance function Z can be plotted on the complex plane. Figure 5.73 Z= vs is is vs (5. Notice that this set of stable poles are at 208 MHz. 5. In Figure 5. The stability performance is thereby dominated by the set of stable poles represented by the green crosses in the figure.1. these unstable zeros lie exactly on top of the unstable poles. we need to use HB simulation with small-signal simulation option activated to perform this simulation. These poles are unstable poles. the same amplifier operates under an unstable condition. .14 − 1. the unstable poles and unstable zeros cancel each other.14 15. and blue circles represent zeros. Table 5. have moved to the right-hand side.2. pink crosses represent unstable poles.74 Figure 5.9 Imaginary (MHz) ± 194 ± 208 ± 259 ± 194 ± 259 Zeros In Figure 5. There are two sets of complex-conjugate unstable poles and one set of stable poles.3.1. However. The previously stable poles at 208 MHz. The green crosses represent the stable poles. however. Now one set of previously unstable poles have moved to the left-hand side of the complex plane. This creates an oscillation at 208 MHz. making the poles unstable. Poles and Zeros of an L-Band Power Amplifier in a Stable Condition Poles Real (x106) 1.53 15. so as one set of previously unstable zeros. which is verified experimentally.9 1. Poles and zeros of an L-band power amplifier operating in a stable condition. 3. Only one set of unstable poles are canceled. Figure 5. Note that Figure 5.4 and Figure 5.2 Kurokawa’s Condition Another start-up condition for oscillation is demonstrated by Kurokawa [51]. as the susceptance crosses the real axis at 208 MHz. the oscillation condition is obtained for negative conductance and the zero-crossing of susceptance with a positive slope. In Figure 5.255 0.6 0.4. indicating unstable operation. Table 5.3.5 correspond directly to the pole-zero analysis in Figure 5. There are two sets of complex-conjugate unstable poles and one set of stable poles. Poles and zeros of an L-band power amplifier operating in an unstable condition.2.75 Figure 5. the conductance is positive.1. Poles and Zeros of an L-Band Power Amplifier in an Unstable Condition Poles Real ( × 10 6 ) 0. Therefore.2 and Figure 5. In Figure 5. as the susceptance crosses the real axis at 208 MHz. which indicates stable operating condition.255 − 35.5 demonstrates the use of this condition to determine stable and unstable conditions of the amplifier. the conductance is positive. the amplifier is unstable due to the other set of unstable poles. .5.2 Imaginary (MHz) ± 196 ± 208 ± 274 ± 196 ± 274 Zeros 5.2. When plotting the real part (the conductance) and the imaginary part (the susceptance) vs.537 − 37. generator frequency. 010 1.4.1E8 2.4E8 2.5E8 frequency Figure 5. while sweeping current generator frequency. frequency demonstrate the use of Kurokawa’s condition to determine the stability conditions.0E8 2. while Figure 5. Power amplifier operating in a stable condition.005 -0.005 -0.000 -0.9E8 2.000 -0. If the graph crosses the real axis with a negative admittance. Again these cases correspond to the stable and the unstable conditions in sections 5.76 0.1.2.005 imag(Ybif) real(Ybif) 0.005 imag(Ybif) real(Ybif) 0.3E8 2. the oscillation is likely to start.2.5E8 frequency Figure 5. Plots of the real and imaginary parts of the admittance function vs. Figure 5.8E8 1.2E8 2.9E8 2. Power amplifier operating in an unstable condition.1E8 2. 0.4E8 2.010 1.0E8 2.8E8 1.5.1. Plot of the real and imaginary parts of the admittance function vs. The analysis is analogous to Nyquist criterion. .010 0.010 0.2. frequency demonstrate the use of Kurokawa’s condition to determine the stability conditions.2E8 2.2.1. 5.1 and 5.3E8 2. the real part of the admittance.7 shows that the amplifier operates in an unstable condition.6 shows that the power amplifier operates in a stable condition.3 Admittance Plot The third tool for detecting oscillations is to plot the imaginary part of the admittance vs. Also the same procedures need to be repeated for the circuit operating in other bias conditions.004 -0.004 0.10 0. based on harmonic balance (HB).05 -0.005 real(Ybif) Figure 5.001 0. imag(Ybif) 0.2. which always lead to the same conclusion.10 -0. It is important to note that the Kurokawa’s condition and the admittance plot techniques are essentially the same techniques.004 -0.003 -0. Admittance plots showing stable conditions of the amplifier.001 0.003 0.005 -0. the boundary between .05 imag(Ybif) 0.003 -0. It is a critical step because the mistakes in formation of frequency basis will lead to errors in the conclusions of the stability analysis.000 0.10 -0.05 -0. The pole-zero identification technique is an independent technique.002 -0. 5. have been proposed for this analysis. Admittance plots showing unstable conditions of the amplifier.00 -0.10 0.004 0.003 0.001 0. which can be used to verify the results of the other two techniques. drive frequency and input power.005 0.005 real(Ybif) Figure 5.00 -0.000 0.6.2 Determination of Stability Contour Different techniques [44][45][46][47][48].77 0.05 -0. In case of variation of circuit parameters.002 0.001 0.002 -0.002 0.7. The use of this approach is very broad.78 stable and unstable operation can be efficiently determined through bifurcation detection on HB [44][45]. In general. Two important pieces of information contained in the largesignal source are the amplitude and the phase of the signal. in some cases.8.1 GHz to 1. One useful feature of this technique is the determination of the phase information of the oscillation signal. . so the bifurcation analysis should be carried out in terms of all significant operation parameters. This global analysis will be applied here to a pushpull power amplifier. Y = 0 . The results are shown in the later part of this chapter. the small-signal admittance matrix is calculated based on large-signal operation. To determine the boundary between the stable and the unstable regions. the AG is a large-signal signal source. Using the two equations Re{Y } = 0 and Im{Y } = 0 . This information cannot be determined from the conversion matrix technique. Using the conversion matrix approach described in the previous section. 5. Since the admittance function is complex. Unlike the small-signal current source in the conversion matrix approach. A schematic of the auxiliary generator applied to a power amplifier is shown in Figure 5. This makes the AG approach more versatile than the conversion matrix approach. two circuit variables can be solved simultaneously. the AG approach is much slower than the conversion matrix approach due to the large-signal nature of the AG.2. the amplifier will operate under different values of bias voltages and different input frequency and input power. the non-perturbation.3 Bifurcation Analysis Using Auxiliary Generator Auxiliary generator (AG) is another useful technique to analyze the behavior of the power amplifier and other nonlinear circuits. and most of the applications are beyond the scope of the thesis. in the band from 1. However. must be satisfied.3 GHz. both the real part and the imaginary part of Y are set to zero. it can also be operated in other modes. . Re{Y ( f a . and Class B.8. such as Class AB. V AG .V AG .2 mode. Y= I AG V AG (5. while the odd harmonics and the 2nd harmonic are terminated like a Class-F-1 amplifier. When backing off from deep nonlinear regions.9 shows the simplified schematic of our push-pull amplifier. The result of the phase information is shown in the later part of the chapter. this amplifier has zero-voltage switching like a Class-E amplifier.79 Figure 5. the admittance function Y is calculated. The amplifier is optimized for a Class-E/Fodd.3 Application to L-Band Power Amplifier Figure 5. The phase information is used to determine whether the oscillation is even mode or odd mode.24) 5. Similar to the conversion matrix technique.2 operation [52]. When operating in the Class-E/Fodd. φ AG )} = 0 (5. φ AG )} = 0 Im{Y ( f a . Schematic of auxiliary generator applied to a power amplifier.23) The non-perturbation condition is solved to determine the amplitude and the phase of the oscillation. In this particular amplifier. One example of the oscillation spectrum is shown in Figure 5.80 Vdd 2nd Harmonic Trap Y = I / Vg1 Vd1 Vg1 Open at f = fin Short otherwise Vd2 Vg2 I Figure 5.10. Simplified schematic of the Class-E/Fodd.2 amplifier. This oscillation is only obtained at certain combination of input power. and drain and gate bias voltages. low-frequency oscillation is observed at around 200 MHz.9. The oscillation frequency shifts slightly at different bias voltages and different input power. no self-biasing oscillation is observed. drive frequency. . During the operation of the Class-E/F amplifier. 5 Input Frequency (GHz) Drain Bias = 14V 20 Spectrum (dBm) Spectrum (dBm) 0 -20 -40 -60 -80 0 0.5 Input Frequency (GHz) Figure 5.81 Drain Bias = 3V 20 Spectrum (dBm) Spectrum (dBm) 0 -20 -40 -60 -80 0 0. with the input power and gate bias voltage fixed.5 Input Frequency (GHz) 20 0 -20 -40 -60 -80 0 Drain Bias = 20V 0.5 Input Frequency (GHz) 20 0 -20 -40 -60 -80 0 Drain Bias = 10V 0.5 V.5V 20 Spectrum (dBm) Spectrum (dBm) 0 -20 -40 -60 -80 0 0.5 Input Frequency (GHz) 20 0 -20 -40 -60 -80 0 0.5 1 1. The oscillation is drive frequency is 1030 MHz.5 1 1.10. The oscillation occurs at about 200 MHz.5 1 1.5 1 1. Mixer-type oscillation is observed.5 1 1. and vanishes when drain bias voltage reaches 20 V. the low frequency oscillation is observed when drain bias is at 4.5 1 1. As the drain voltage increases. . Oscillations in L-band power amplifier.5V Drain Bias = 5.5 Input Frequency (GHz) Drain Bias = 4. In the plane defined by fin and Pin.25) Vd=10V Vd=12V Vd=14V Input Power (W) Unstable Stable Constant fin = 1. Measurements are superimposed.VD )} = 0 (5.15 Input Frequency (GHz) Figure 5.14 GHz.05 1.VG . The boundaries between the stable and unstable regions based on globalstability analysis of the amplifier.VG .11.1 1. The frequency fin is swept. the . for different operation conditions. the instability region shrinks due to reduced feedback through the gate-drain capacitance (Cgd). The analysis is performed for different VD and constant VG = 3 V. no instability is obtained at any of the considered bias voltages. at each step. As confirmed by pole-zero identification.VD )} = 0 Im{Y ( f a . and markers indicate measurement points. In agreement with the pole-zero identification technique. The second analysis is carried out in the plane defined by VG and VD (Figure 5. Pin and the oscillation frequency fa. which varies along the locus. 5 4 3 2 1 0 1 1. with the results of Figure 5. obtaining the loci of Figure 5. Lines indicate simulation results. the instability occurs at medium input power.82 The above system is solved through error-minimization or optimization procedures.03 GHz and two typical operation Pin values have been considered. where the gain is the highest. For fin > 1. As the drain-bias voltage increases. combining HB and the conversion-matrix approach. solving: Re{Y ( f a . calculating.12).12.11. The use of bifurcation analysis enables efficient determination of the element values of each stabilization network.4 Stabilization Techniques The actual design goal will be the stabilization of the amplifier. will be helpful to devise a proper stabilization technique. The boundaries between the stable and unstable regions based on globalstability analysis of the amplifier. Class B. together with the analysis of the oscillation mode. However. and Class C. the instability region is smaller for the Class-C operation. oscillation vanishes due to smaller feedback capacitance.12. for different operation conditions. . In the plane defined by VG and VD. and markers indicate measurement points. which corresponds to lower VG.83 amplifier is unstable inside the different loci. The performances of the resulting stabilized amplifiers will be compared. Three different techniques will be considered here. neutralization capacitors. in terms of output power and efficiency. and feedback resistors. Lines indicate simulation results. 5. 30 Class C Drain Bias (V) 20 Pin=4W Class B Class AB Pin=5W Stable 10 Unstable Stable 0 1 2 3 Vth 4 5 Gate Bias (V) Figure 5. based on the use of odd-mode stabilization resistor. The unstable behavior is observed in different operating modes: Class AB. and the knowledge of the instability regions in the parameter space. At higher VD. three different stabilization techniques will be considered. Thus. the stabilization resistor is in parallel with the gate of the transistors. in order to avoid the HB convergence to the unstable periodic solution at fin [44]. Using the half-circuit analysis for the odd-mode oscillation at 200 MHz. inductors may be used to block the signal at the operating frequency. fin = 1030 MHz. The odd-mode oscillation can be eliminated through the connection of a resistor between the gate terminals of the two transistors shown in Figure 5. VD = 7 V.5 V.4. where the amplifier behaves as a self-oscillating mixer. we see an odd-mode oscillation at 200 MHz. for VG = 3.1 Stabilization with an Odd-Mode Stabilization Resistor Based on the result shown in Table 5.84 The nature of the oscillation has been investigated obtaining the steady-state solution within the unstable regions. there is an odd-mode oscillation. Thus. Since the oscillation frequency (200 MHz) is sufficiently lower than the operating frequency of the amplifier.13. . at the two fundamental frequencies fin and fa. The voltages exhibit a phase difference close to 180º at both fin and fa. Table 5. the input power from the input drive will not be dissipated in the stabilization resistor.3.3. The transistor harmonic voltages at the input-drive and oscillation frequencies are compared in Table 5. An auxiliary generator (AG) has been used. Pin = 3 W. thereby shunting the oscillation signal to ground.3 The phases of voltages at the gate and drain terminals Vg1 0° −137° Vg2 180° 43° Vd1 −98° −84° Vd2 72° 96° fa (200 MHz) fin (1030 MHz) 5. In the following. 85 Figure 5. Due to the continuity of the system. the maximum allowed value for the stabilization resistance is 200 Ω. Schematic of stabilization circuit using odd-mode stabilization resistor. The maximum allowed value for the stabilization resistor R is obtained by tracing the oscillation boundary in the plane defined by R and one of the four circuit parameters. this provides information about the required resistance for a general stabilization of the amplifier. the amplifier must operate outside the instability regions for all the fin values. The amplifier is unstable on the right-hand side of the represented loci. Note that the selected bias values correspond to the edges of the operation intervals. for all the operation conditions. . Thus.14. the considered parameter is fin and the oscillation boundary is determined for different Pin and bias values.13. In order to avoid the instability. In the analysis of Figure 5. sweeping the bias voltages.5V Vg=4V Pin=4W Vd=7.95 0 Stable Vg=4V Unstable Pin=4W Vd=5V Vg=4V Pin=5W Vd=5V Vg=4V Pin=4W Vd=5V Vg=3V Pin=5W Vd=5V Vg=3V Pin=5W Vd=7. . the amplifier is unstable at certain operating points. Stabilization with an odd-mode stabilization resistor. Typical operation conditions have been considered in these simulations.10 1. because the curves cross the real axis with negative conductance values. the curves shift to the right-hand side of the complex plane. Different curves in the plots represent different operating conditions. input power. When no stabilization resistor is implemented. and the input frequency.14. As stabilization resistors are implemented.00 0. the amplifier is globally stable for all operating conditions.86 1. As the stabilization value reaches 200 Ω. The global stabilization is verified using the admittance plots (Figure 5.15 Input Frequency (GHz) 1.05 1.5V Vg=4V Vg=3V 200 400 600 800 1000 Stabilization Resistance (Ω) Figure 5.15). 01 0.01 0.03 -0.03 -0.02 -0.10 -0.02 0.03 Real (Y) Imag (Y) 0.02 -0. 5.05 -0.4.01 0.10 0. Since the oscillation is odd-mode.10 0.05 Imag (Y) Imag (Y) 0.00 0.00 -0.02 0.03 Real (Y) 0.10 -0.10 -0.10 0.00 0.2 Stabilization with Neutralization Capacitors In push-pull configurations. Effectively.05 R = 1000 Ohm -0.03 Real (Y) R = 500 Ohm R = 200 Ohm Figure 5.01 0. The two signals at 200 MHz therefore are cancelled to achieve stabilization.05 0.01 0.03 -0.03 Real (Y) No stabilization 0.02 0.02 0.00 0. a negative capacitance is added in parallel to Cgd.87 0. For clarity purposes.00 -0.05 Imag (Y) 0. it is clear that the feedback through the neutralization capacitor is 180o out of phase with the feedback through Cgd. only a portion of the representative curves are shown.01 0. . Admittance plot for various stabilization resistances.00 0. neutralization capacitors can be connected between the gate and drain terminals of the opposite transistors to cancel undesired feedback through Cgd shown in Figure 5.05 -0.02 -0.16.10 0.03 -0.01 0.00 -0.10 -0.01 0.02 -0.00 -0.05 0.05 -0.15. the neutralization capacitance should be larger than 25 pF. the entire set of bifurcation loci must be taken into account.17. From this global analysis. the oscillation boundary will be traced on the plane defined by Cn and fin. To determine the minimum capacitance value required for stable operation. Schematic of stabilization circuit using neutralization capacitors. considering different Pin values and bias conditions.16.88 Figure 5. To ensure stable behavior for all the operating conditions. For clarity. only two loci have been represented in Figure 5. . .89 1.05 Vd=7.5V Vg=4V Pin=5W Stable 1.00 0 5 10 15 20 25 Neutralization Capacitor (pF) Figure 5.20. a resistor and a DC-blocking capacitor are connected between the gate and the drain terminals of the same transistor. The bifurcation-analysis technique indicates the maximum value of stabilization resistance of 90 Ω.3 Stabilization with Feedback Resistors In order to reduce the positive feedback.17. For clarity reasons. only two representative sets of curves are shown. shown in Figure 5. 5. which is about five times the oscillation frequency. as parasitic inductances of the two elements provide high impedance at fin. Stabilization with neutralization capacitors using bifurcation loci.15 Input Frequency (GHz) Vd=5V Vg=4V Pin=5W 1.10 Unstable 1. shown in Figure 5. Only limited power is dissipated. These parasitic inductances do not have a significant effect on the feedback resistance at fa.18.4. 4. The odd-mode resistor is implemented in the .15 Input Frequency (GHz) Pin=5W Unstable Pin=4W 1. Typical operation conditions have been considered in these simulations.20 shows the comparison of the stabilized-amplifier performance for the three different stabilization techniques. In this particular amplifier.19. neutralization is not easy to implement due to layout constraints. but the PAE is reduced by 6%.18.05 Pin=3W 1. The resistive stabilization techniques show little change in performance.10 Stable 1.90 Figure 5. Stabilization circuit using feedback resistors and DC-blocking capacitors.00 0 100 200 300 400 500 Feedback Resistance (Ω) Figure 5. 5. 1. The neutralization capacitors improve the gain of the amplifier by about 2 dB. Stabilization with feedback resistors.4 Comparison of Performance Figure 5. The measured performances are almost identical.20.21 shows the gain and the PAE at 1210 MHz before and after applying the odd-mode stabilization. Measured amplifier performance before and after applying odd-mode stabilization resistor of 150 Ω. 15 70 60 Gain (dB) 40 30 5 Solid Line: unstablized PA Markers: stabilized PA 20 10 0 0 20 40 Output Power (W) 60 80 0 Figure 5. Figure 5.91 amplifier.21. 14 80 70 Drain Eff (%) Gain (dB) 12 unstablized feedback resistor neutralization capacitor odd-mode resistor unstablized feedback resistor neutralization capacitor odd-mode resistor 60 10 50 8 0 20 40 60 80 Output Power (W) 40 100 Figure 5. PAE (%) 10 50 . Simulated amplifier performance after applying three different stabilization techniques. three different stabilization techniques have been compared. the values of the stabilization elements ensuring stable behavior for all the operation conditions have been determined through bifurcation analysis. Four parameters—two bias voltages.5 Summary In this chapter. For each approach. the global stability analysis of an LDMOS amplifier has been presented. .92 5. After determination of the oscillation mode. the input power and the input frequency—have been considered. current state-of-the-art power transistor technologies are reviewed. The performance of these technologies is compared.2 ×10 7 9 . are discussed. At the same time. can be used to achieve high output power at higher frequency.1 New Transistor Technologies In this section.9 2.5 SiC 2. The new immerging devices. Key Properties Comparison for Microwave Power Transistors Properties Bandgap (eV) Thermal conductivity (W/oC cm) Breakdown field (KV/cm) Saturated electron velocity (cm/sec) Relative permittivity Si 1. particularly SiC and GaN.5 3× 10 5 1×10 7 11. Because of these properties.9 GaAs 1. 6. The table below compares the most popular semiconductor materials for discrete power amplifiers from HF frequency up to 3.12 1.93 Chapter 6 Future Opportunities As discussed in Chapter 1.5 × 10 6 2 ×10 7 10 GaN 3. has opened new horizons for better performing power amplifiers.3 2×10 6 2. they achieve much higher power density than Si and GaAs.45 1. such as SiC and GaN. such as DAT. The development of new semiconductor devices. It is no surprise that improvements can always be made for the future applications and technologies.1. It is clear that SiC and GaN wider bandgaps and higher breakdown field. as well as other transformers and baluns. more efficient power combining techniques.54 4×10 5 1×10 7 12. and the preliminary results are presented. discrete high power amplifiers have many applications in the fields of wireless communications and space technologies.5 GHz. A singled-ended Class-E amplifier based on the SiC MESFET is built.42 0.86 4. Table 6. which is higher than that of typical GaAs devices. thermal conductivity. efficiency. High drain bias voltage is preferred in the class-E/Fodd power amplifiers. but they are several times higher in cost. but can handle more current than the Si devices. They operate at around 12V. reliability. availability. . which are also compatible with circuit simulation software like Agilent ADS. Recently.1 Si and GaAs Devices There are many different choices of RF power devices between 1 and 2 GHz. VDMOS achieves nice performance. which are operated at 28V like LDMOS. cost. The modeling of LDMOS power transistors is quite mature. input and output impedances. but at higher frequency above 2 GHz. on-resistance. GaAs HBT’s and MESFET’s have shown superior performances beyond 2 GHz. Si VDMOS and LDMOS have the lowest cost of all RF power devices.1. The performance of a GaAs power amplifier at 1 GHz is similar to LDMOS amplifiers. They have lower power density than GaAs power devices. Below 500 MHz. GaAs amplifiers still hold some advantages. provide excellent large signal models. power gain. VDMOS and GaAs based power devices including GaAs HBT’s and GaAs MESFETS. Some manufacturers. the operating voltage is around 28 V. etc. there is development of high-voltage GaAs devices.94 6. GaAs HBT and MESFET have the higher power densities than Si VDMOS and LDMOS. The thermal conductivity of GaAs is not as good as Si. output capacitance. Currently. while LDMOS has been the most widely used technology from 500 MHZ to 2 GHz. such as Motorola. Both the small signal and the large signal models are fairly accurate. the dominating technologies in L-Band high power amplifiers are Si LDMOS. The selection criteria for such devices include power density. bias voltage. However. SiC MESFETs are very promising power devices in RF frequencies. One major consideration of power devices for switching power amplifiers is the output capacitance. high power density. Designers have to use many crude models to estimate the performance of the amplifier. Also. However.95 6. Even though new techniques have been developed in this work to exceed this limit. we see that the output capacitance of the Freescale LDMOS transistor is 8 pF at the operating . As we take a closer look at the specifications in Table 6. the modeling of these devices is not as mature as Si and GaAs devices. The drawback of these devices is that they are still not as reliable and are not widely available commercially. The lack of accurate large signal models significantly increases the difficulty and the length of time to do the power amplifier design. high thermal conductivity.1. both devices apparently have the same size package. power devices are typically large in size. Traditionally. Smaller SiC devices lead to high input and output impedances. thereby having very large input and output capacitances and low input and output impedances. They also limit the bandwidth and increase the complexity and the size of the power amplifier. Both devices have nominal output power of 10W. high saturated electron drift velocity. Low input and output impedances increase the difficulty of the design of the amplifier.2 SiC and GaN Devices Another important development in the last several years is the emergence of wide bandgap semiconductors SiC and GaN for high power RF applications. Because of that. the operating frequency of the switching power amplifier is limited by the output capacitance of the device. the SiC devices are significantly smaller than LDMOS devices and GaAs devices for the same output power. As we can see from the photo.1 shows the comparison of Lband power devices: a Freescale Si LDMOS and a Cree SiC MESFET. This property greatly simplifies the input and the output circuits of the power amplifier.1. The costs of these devices are several times higher than their Si and GaAs counterparts. The output capacitance of the device is smaller than LDMOS and GaAs devices. and in the case of SiC. Figure 6. such as high electric breakdown field. These devices exhibit superior properties. a lower output capacitance can be advantageous. They have much higher power density than Si LDMOS and GaAs. which has an input resistance about 1 Ω. It is now possible to build a broadband 5W PA from 20 MHz to 2.1.5 GHz. Figure 6.9 pF at the operating voltage.96 voltage and the output capacitance of the Cree SiC MESFET is 1.0 pF at Vds = 26 V 26 V SiC MESFET 120 V 10 W 1.5 Ω. Comparison of Key Specifications of LDMOS and SiC Devices Properties Maximum VDS 1dB Output Power Output Capacitance Operating Voltage Si LDMOS 65 V 10 W 8. and improve the efficiency of the power amplifier. The input resistance of the device is about 5. using one SiC transistor. The low output capacitance property can significantly simplify the output matching circuit. Table 6. .2.2. This comparison shows that there is a great potential for broadband amplifiers using these SiC devices. Photos of two 10W L-band power transistors: Freescale MRF282S Si LDMOS (left) and Cree CRF 24010 SiC MESFET (right). This impedance is about 5 times higher than the Si LDMOS counterpart.9 pF at Vds = 48 V 48 V The measured input and output impedance (provided by Cree) of the SiC MESFET are shown in Figure 6. GaN . and GaN devices. In order to design power amplifiers with SiC transistors. GaN devices suffer from low thermal handling capabilities.5 Ohm Input Resistance Figure 6.97 Output Impedance 20 – j 17 5. The only model provided is the S-parameter data at certain bias points. SiC has an advantage over GaN in thermal conductivity. designers need to make their measurements of the devices in order to gain insights that are critical for power amplifier design.2. Currently. Therefore. The GaN HEMT has the highest power density among all devices. There is no high frequency large signal model available from the manufacturer. Inc. GaN HEMTs also have superior current handling capability. The only power device outputs 60W per transistor. However. Measured input and output impedance of the SiC MESFET. While both SiC and GaN have very high power density. Also. SiC has much higher thermal conductivity than Si LDMOS. The modeling of the SiC is not mature. This device is suitable for operating at relatively high temperature. GaAs devices. which can output over 200 W. The design cycle may be longer due to the lack of accurate models. The output power capability is not nearly as high as the state of the art LDMOS and GaAs power devices. they are grown on the SiC or Si substruates. the only commercially available SiC power transistors are from Cree. Layout of SiC Class-E power amplifier .1.8 mm Figure 6. Since the GaN devices have the highest power density in the group.3. DC measurement of the device is performed. such as lack of large signal models and reliability problems. and the on-resistance is extracted from the DC curves. The layout and the photo of the amplifier are shown in Figure 6. Recently. we may expect to see great performance by these devices.98 HEMT shares some of the problems with SiC devices. there are some commercially available GaN HEMT devices by Eudyna. Vg SiC RF in RF out 25.4. Due to the lack of nonlinear model of this device. it is difficult to optimize a push-pull design in a short period of time. The Class-E amplifier is then built and tested.4 mm Vd 50. In particular.3 SiC Class-E Power Amplifier The active device used in the Class-E amplifier is Cree CRF-24010. The nonlinear output capacitance of the amplifier is approximated using a reverse-biased diode model.3 and Figure 6. 6. the tuning of the second harmonic and third harmonic are difficult. Output Power 25 Gain (dB) and Power (W) 20 15 10 5 0 900 Gain PAE 70 60 PAE (%) 50 40 30 20 1300 1000 1100 Frequency (MHz) 1200 Figure 6. .4. The peak output power is 19W with a power gain of 9 dB. The preliminary performance of the Class-E amplifier is shown in Figure 6.5. from 980 MHz to 1200 MHz. It is worth noting the bandwidth of the amplifiers. Photo of Class-E SiC power amplifier. the gain remains very flat over a broad frequency band.99 Figure 6. Measurement bandwidth performance of the SiC power amplifier. Even without an accurate model. The peak PAE is 65%.5. At microwave frequencies. The disadvantage is the cost is high and the process is time consuming. Some of the models used in designing the Class-E/F amplifiers described in the thesis are based on this approach. The second approach is the opposite extreme of the first approach.6. and the design of the output termination network is based on the . it is important to include the package inductance of the device. Most of the L-band high-power amplifiers are based on one of the following models. Another problem with the approach is that the table-based model does not provide equivalent circuit model. such as nonlinear vector network analyzers. The simplest model is based on the assumption of a Class-AB design. often table-based model. Another approach to switching-mode amplifiers is the simplified switch model shown in Figure 6. This kind of the design is clearly not accurate. The transistor output characteristics are modeled using a simple switch in series with an ON resistance. Also. It is well known that the large-signal behavior of the transistor is very different from the small-signal behavior. Extensive tuning has to be performed manually after the building the circuit. The advantage of this approach is that the nonlinear output capacitance can be modeled as a function of drain bias voltage.100 6. The advantage of the approach is that the model is accurate for a wide range of conditions. One set of linear Sparameter is measured at one single bias point. and the input and output matching are designed based on the linear matching network. which is needed for useful insights for the circuit design.2 Modeling for Switching-Mode Amplifiers It may seem strange that almost no transistor modeling has been discussed up to this point in the dissertation on power amplifiers design. Then a complex system is used to collect all measurement data to provide an accurate. the measurements are performed at an exhausting range of conditions. Expensive equipment. and in parallel with the device output capacitance. The simple answer to this is that there is no easy route to obtain an accurate nonlinear model at microwave frequency for harmonic balance simulation. is used. and many iterations of re-designs are typically required. Simplified switch model for the input and the output circuit of the transistor. The voltage and current waveforms can be simulated and optimized easily to achieve high efficiency. The resistive dissipation of the power amplifier is directly related to the onresistance of the power amplifier. Lg Cgd Ld Cgs Ron Cds Figure 6.7. Switch model of the transistor output circuit. The difficulty with this approach is that the measurement of the output capacitance is difficult. Ld Cds Ron Figure 6.101 nonlinear output capacitance and the package inductance. Lower on-resistance translates directly to lower resistive . The on-resistance of the power device is an important property of the switching power amplifiers. It is necessary to come up with a set of simple measurements and extract the critical nonlinear elements in the transistor model and optimize the waveforms of the amplifier based on the equivalent circuit model shown in Figure 6. it is difficult to separate the measurement of the output capacitance Cds from the feedback capacitance Cdg.7.6. At this frequency. 6. A discrete version of DAT in Class-E/F mode is implemented at 29 MHz to achieve 2. The on-resistance can be determined by measuring the DC IV characteristics of the device. The nonlinearity of the capacitance can be modeled by fitting a curve for a variety of bias conditions. we see that since the L-band power transistors are much larger in size. discussed several times in the thesis. and feedback capacitors can be extracted from S-parameter measurement using the network analyzer. since DAT structure combines the output power of eight transistors. Using the typical DAT.3. 6. the Distributed Active Transformer is a promising candidate for effective power combining and impedance transformation. Ichiro Aoki’s original designs are integrated CMOS amplifiers at 2. If we assume that theoretical designs indicate that it is possible to combine output power of eight transistors. However. .1 Challenges in Discrete L-band DAT Perhaps the biggest challenge in designing an L-band discrete DAT is the layout problem. One solution to this is 1 This portion of the work is collaborated with Sébestien Lasfargus. The input.4 GHz [4] and then 1. and still achieve higher total output power than the push-pull amplifiers designed in this thesis.9 GHz. the layout with larger transistor packages like MRF 284 used in the amplifier is extremely difficult. we can afford to use smaller transistors with less power for the power combining. the operating frequency of the amplifier is limited by the output capacitance of the transistors. If we calculate the electrical length of the previous DAT amplifiers.7 kW of output power with high efficiency [35].102 loss in the amplifier and high efficiency. A natural question is: can this discrete version of DAT be implemented at L-band? We will look at some of the challenges and possibilities in this section. output.3 Discrete L-Band DAT1 As introduced in Chapter 3. the size of the DAT may be too large for an ideal operation. The second challenge to implement as a design is the high device output capacitance. and the simulated PAE is about 65%. 6.103 similar to the technique discussed in Chapter 3 by inserting an external capacitor at the output of the DAT as shown in Figure 6.2 Layout and Simulation Preliminary layout of the discrete L-band DAT using eight Freescale MRF 282 transistors was simulated in commercial microwave simulator. The simulated output power is over 120W.8. Vdd + + + - - Output - Vdd Figure 6.8. Vdd + Vdd + - . We can use this external capacitor to increase the operating frequency of the amplifier. A Class-E driver stage may be added to improve the gain and the input matching of the amplifier.3. Output circuit of the PA with DAT and an external output tuning capacitor. 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